Corporate pilot with ZMA expressed concern regarding the controller's performance; attributed to the controller operating multiple frequencies simultaneously with all aircraft having difficulty understanding instructions.

Narrative

While flying the SSCOT 1 arrival into TMB; ATC changed our arrival routing to fly direct to KARTR Intersection; then to EYW and join CURSO 2 arrival because of weather. Shortly after this change; we were directed to contact Miami Center. We heard the ATC Controller very stressed out issuing clearances and instructions to too many aircraft and at one point; he started requesting patience from everybody because he was working 'SEVEN FREQUENCIES AT THE SAME TIME'. What followed after this was a complete chaos on the frequency because everybody was calling at the same time; blocking each other; trying to get their needs done; like turning to avoid weather; descend and so forth. The Controller ignored several calls; not only from us; but from some other aircraft he was handling. All of the sudden; the weather was not a factor anymore and we ended up just 46 NM north east of EYW in clear weather and in perfect position to proceed to our destination. I kept calling ATC; but he ignored my calls several times until he finally gave me clearance to fly direct to the airport. This is not the first time a similar situation happens. FAA is understaffed and this scenario could be very dangerous at certain point. This is a potential disaster just waiting to happen.