The FAA sets the volume that can operate over the affected routes. This is usually done by either closing routes or instituting miles-in-trail restrictions. They'll issue EDCTs (Expect Departure Clearance Times) to flights filed on the routes.

Every flight can operate. Eventually. But delaying many flights, many hours each, isn't a workable plan. What about the flights that the affected airplanes and crewmembers were supposed to operate after the delayed flight? You'll have all the south Florida flights sitting at EWR, LGA, JFK, IAD, DCA, CLT, ATL, etc. all day waiting for their slots, and all the people who were supposed to fly on those airplanes, and by those crews, for the rest of the day sitting looking at their empty departure gates.

Jacksonville Center is one of the ATC facilities that has been hit hard by staffing shortages. This reduces the amount of traffic they can handle on days like today. In the past, with more reasonable staffing levels, today's weather would not have resulted in such severe ATC restrictions as it does today. Delays were fewer, and shorter, and affected fewer flights.

Watched the NASS page for a few days and see what restrictions result from the weather-triggered ATC delays.

https://nasstatus.faa.gov/