Air carrier Captain reported flying into a normal controlled airport; but Tower was closed due to COVID and having numerous issues in the air and on the ground with other aircraft.

Narrative

On arrival; approximately 30 miles north of ZZZ; we were descending to 6;000 ft; when Approach informed us that the Tower would be closing in 5 minutes without explanation. We had prepared and briefed a visual approach to Runway XX per the ATIS; with no NOTAMs pertaining to a Tower closure. I was the Flying Pilot; and we decided to slow down and configure the aircraft early so that we could keep our heads up and watch out for traffic. At approximately 10 miles north of the airport; Approach asked us if we had the airport in sight; we acknowledged; and they cleared us for a visual approach to Runway XX. We switched to the CTAF frequency; announced our position; altitude; and intentions; began a gradual descent to 4;000 ft. and entered directly into the traffic pattern on a left downwind. The CTAF frequency was very active with aircraft announcements for simultaneous departures and landing to BOTH intersecting runways. We were inundated with TCAS targets coming from all directions; altitudes; and proximity; from as little as 500 ft. below us and 700 ft. above. We observed targets that seemed to be popping out of nowhere; over or alongside mountains; out of valleys; and several that were just flying low in the valley itself. All unannounced. It was almost like flying in a beehive. Our radio calls were continuous; as we announced our position; altitude and intention. We entered a left base to intercept a 10 mile final; and I began to have reservations about conducting an approach with so much traffic. I began to contemplate abandoning the approach altogether and started to consider where a plausible alternate might be; but decided to continue to 5 miles out as my decision point. At about 7 miles; a Cessna in a close in pattern announced that he was going to be making a left base turn to Runway XX; essentially right in front of us. We made several more calls advising our position and distance from the airport; and I became virtually certain that we would need to abandon the approach; but was waiting to acquire the aircraft visually before going around. Moments later someone using a ground-based radio (Airport Operations) advised the aircraft who was about to turn in front of us to extend downwind since we were on short final. The aircraft stated that he had us in sight and would continue downwind and land behind us. We could also hear other aircraft throughout the approach making sporadically coherent/incoherent announcements for departures and landings to Runway YY; with various traffic pattern variations; but none seemingly aware of our approach to the intersecting runway; or the spacing that might be necessary to accommodate safe separation.We landed; turned off at XX2 to Taxiway XX to the ramp. We announced that we were clear of the runway and would be taxiing across the approach end of Runway YY on A. We heard a helicopter announce that he was on a tight right base turn to Runway YY; but couldn't see him because he would have been above and behind us. We scanned the area and proceeded; just as the helicopter was cut off by a Cessna landing straight in to Runway YY. That aircraft went over the top of us; and we saw him outside the FO's (First Officer) side window as he passed over the top of us at about 50 ft. We couldn't believe it. We taxied into the ramp; and parked. We were both shaken by the stressful environment. As we began deplaning; I noticed an airport vehicle parking just in front of our left wing and the driver got out and made visual contact with me in the cockpit; so I went out to speak to him. He advised me that the Tower was closed due to COVID; and that it would be closed until XA:00 am the next day. I asked him if he had been observing the traffic around the airport; and told him that someone flew over the top of us on the approach end of Runway YY. He said that he had been listening to the radio and watching the traffic; relating that he had overheard an argument between two aircraft attempting to land Runway ZZ & YY at the same time in opposite directions. He described the conditions as total chaos with a 'bunch of idiots' who didn't know what they were doing. He went further to say that the airport was never designed for this type of traffic; as it was simply a modified military airport. I told him about the traffic conflicts we had experienced on landing; and we both agreed that operating a 121 category aircraft in the current conditions without a Tower in operation was not safe. I returned to the cockpit; the First Officer and I debriefed; and together we concluded that based on the current volume of traffic; operation into ZZZ without a Control Tower was simply unsafe for our category of aircraft. Both of us agreed that our scheduled return leg from ZZZ1 would require us to fly almost directly into the setting sun; at a time when people would be focused on watching the sunset over the [surrounding areas]; and at a time of the day when aircraft traffic volume was sure to be exceptionally high with a variety of different aircraft types. Without an operating Control Tower managing traffic flow to the two intersecting runways; providing aircraft separation and advisories; we concluded from our first-hand experience; that the risks associated with continuing our flight within our scheduled time frame was simply unsafe.I called our Dispatcher to advise her of the Tower closure; what we had experienced on our arrival; and our concerns for safety on the return flight into ZZZ from ZZZ1 within our scheduled time frame. I explained to her that we would be willing to fly the plane out of ZZZ given our capability to climb quickly away from the potentially conflicting traffic and congestion; but that we would not be willing to return given the current conditions. She said that she was going to reach out to her Supervisor; who I believe ultimately cancelled our flight; but we never received official confirmation from anyone.Shortly thereafter; I received a call from my Chief Pilot with an inquiry about our situation. I briefly described what we had experienced; and that we didn't believe it was safe to operate our return flight into ZZZ in the current conditions. He explained that we operate in uncontrolled airport conditions all the time; and I agreed. He asked me if I had the capability to predict air traffic volume; and I told him I did not. He then asked me if I was 'shutting down the operation'; and I said that I was not; but that I personally would not be willing to return to ZZZ based on the current conditions. Clearly frustrated and unsupportive of my decision; He requested an [report] and informed me that; 'this would not be the last I heard of this'. In summary; I refused a return flight segment to ZZZ in compliance with regularly scheduled operations for an uncontrolled airport due to safety concerns rising from traffic saturation in the terminal environment based on current conditions; the unscheduled closing of the airport Control Tower; and loss of ATC services that are normally available at this time of day. While we did not have a crystal ball that would have enabled us to see or anticipate what the traffic volume would be on our return; given the short round trip; we did not anticipate that it would change significantly over time; and rather than returning to what we believed would be similar conditions to those we had just experienced; we notified the company of our unwillingness accept what we believed were unacceptable risks to safety of flight.Unscheduled Tower closure due to COVID; loss of ATC services; high volume of aircraft operating in the vicinity; utilization of two intersecting runways operating simultaneously; poor situational awareness and communication by GA aircraft operating in the terminal environment; lack of adherence to standard traffic patterns and altitudes among by GA aircraft in the terminal environment. I also believe this was sort of a perfect storm situation; in that with the conditions being perfect for flying; the time of day; the greater ZZZ environment was unusually congested with GA aircraft enjoying aviation. While we typically would have no difficulty or safety concerns operating in this environment; this particular day and the lack of ATC services in this environment presented conditions that in my opinion were unsafe due to the differences in size and speed of our aircraft with respect to others operating in the same proximity.I believe the airport could have listed a NOTAM prior to the unscheduled Tower closure that may have informed pilots that the environment was going to become uncontrolled; allowing them to possibly make alternative choices for their operations; and/or plan ahead for standard traffic pattern entry procedures.