An air taxi Captain descending on a STAR reported a NMAC with a VFR aircraft.

Narrative

We were on the ZZZZZ arrival approaching ZZZZZ1 waypoint and traffic was called at 11:00 O'clock about 5 miles. It was VFR traffic skirting the edges of the airspace and not talking to anybody; but his transponder was reporting position and altitude. I was seriously considering asking for a vector for traffic but then I was contemplating whether the traffic was converging or was going to pass around us. The turn at ZZZZZ1 is to the left so I'm wondering if that is going to put us closer to the traffic. I wasn't sure which direction the traffic was moving. TCAS traffic alert is issued and shortly after TCAS RA with monitor vertical speed". I then acquired visual contact with the traffic as he passed directly under us from left to right. ATC issued a traffic alert and right turn to a heading of 260. ( about a 45 degree turn ) The heading assignment and alert from ATC were both issued as we were passing over the traffic; therefore useless and too late to do anything. We were in the active RA as ATC was issuing the heading. I read back the heading and at the same time notified ATC of the RA. We passed directly over the traffic with 0 horizontal clearance and 400' vertical clearance. Suggestions: At the time of incident; traffic was relatively light for ZZZ. ATC knew that the traffic was there well in advance. They could have issued a heading and provided separation well in advance while it was still possible to do something about it. But; instead they chose to just talk about the traffic. In hindsight I should have asked for a vector early on. I know this because I've seen it happen too many times. The difficulty is that irrelevant traffic information is thrown at you all day long ( aircraft that are not really a threat ). Then when traffic is a legitimate threat it's handled by ATC the same way. You try to figure out how much of a threat it really is or isn't and then it's too late. I know this is not uncommon and it's not unique to ZZZ. It happens too often. It happened to me in City X not too long ago and I didn't file an report. We all just think; well that's life; that's how they do things. This is contrary to common sense. Don't just sit and yak about where the traffic is; just give me the heading."