An air carrier Captain believes frequency and traffic congestion contributed to ATC's failure to position his aircraft to a point from which a stabilized approach could be flown. A go around was initiated.

Narrative

We were on a 120 heading with extremely confusing and congested ATC radio communications on Miami Center. The situation was complicated by numerous recreational aircraft calling for assistance which frequently resulted in broken or garbled transmissions. We were cleared to BOBIO and to pick up the WLACE Arrival. This ATC clearance was issued with the Captain (pilot not flying) off frequency to talk with Flight Attendants about ride conditions into arrival city. The First Officer (pilot flying) misinterpreted BOBIO as another point on our original clearance and proceeded to plug and execute those instructions. Captain challenged the First Officer and both agreed we needed ATC clarification.Due to ATC overload; several minutes passed before we could interject a radio transmission. After barging in on ATC to receive clarification; we proceeded to our new arrival point and clearance into our arrival city from our original clearance. Upon reaching BOBIO and our new arrival; we received TCAS RAs from recreational aircraft and were left at 6000 AGL; 14 miles from Runway 10L. The Captain decided that the stabilized approach criteria were not met in the 'slot' and we were required to execute a go-around at 1000 AGL. Simply put; this scenario was created by an overloaded Miami ATC and random recreational aircraft with little regard or awareness for traffic flow into 3 major international airports. This was as bad as I've seen it in civilian aviation and I hope to never experience this again. The ATC Controller was very professional and competent just overloaded to the demands of his in flight Customers. This is a safety risk! [This Facility needs] better staffing and resource management and better control of recreational flight in congested approach corridors. Last; an ATC frequency should never be congested to the point where a Captain cannot receive clearance clarification in a reasonable time period.