Center Controller reported issues with a re-route for an aircraft on the ground; that would travel 1;400+ miles.

Narrative

I was working the CIC (Controller in Charge) position in Area X; when I received a call from ZZZ TMU (Traffic Management Unit) manager Name. She informed me that Aircraft X; still on the ground in ZZZ; was going to depart into X Sector's airspace for ZZZ on Jet way routing. She said he wouldn't be able to fly that routing and would need to be issued a re-route on alternate route. I asked her why; if the aircraft was still on the ground; why ZZZ Tower couldn't issue the route; to which she responded 'BECAUSE HE'S NUMBER ONE FOR TAKEOFF' and hung up.Considering the request would place the aircraft in Area Y; I walked over and told Name 1; the Area Y CIC to coordinate with the Sector Y controller to effect the change. The pilot subsequently queried the controller why he was being issued the re-route.When she called the TMU supervisor; she said the re-route was due to weather 'in Florida'. IN FLORIDA.Asking controllers to do things that are contrary to our safety-based mission is a reoccurring situation with this particular individual.In this case; we had weather; deviations; turbulence; and icing in and around ZZZ on all departure routes. The SAFEST place to issue an aircraft a re-route is when it is on the ground; not moving. In fact; we even spent a lot of money at ZZZ constructing a midfield taxiway to provide controllers with the flexibility to move aircraft in and around active runways safely in situation *just like this*.Instead; we've made it a routine habit to launch aircraft and ask pilots to increase cockpit workload and distraction by adding unnecessary heads-down time to re-program Flight Management Systems to accommodate ineffective TMU systems; restrictions; and coordination. This also creates the need for the pilots to re-calculate fuel (again; something that should be done on the ground if at all possible) and deprive them of the opportunity to load addition fuel on the aircraft if they deem it necessary because of the new route.