Sometimes you can, but that requires that the adjacent sectors, and facilities, have the excess capacity to accept the rerouted traffic.

If you had only one flight flying around the country, it would rarely be significantly delayed due to weather. There is very little weather that we can't fly through or go around. The problem is that weather reduces the available airspace which reduces the national airspace system's overall capacity below demand. That is what produces the delays. Some things can be fixed, such as ATC staffing, but others are more difficult. We don't have the technology to safely put airplanes much closer together than they are today.

Take a look at the RADAR pictures that was posted just below your message. That's why they couldn't re-route around Jacksonville.