Maybe immobilizing it assists with the recovery time? (disclaimer: I have no idea).
Foot/ankle injuries can be funny sometimes.
I'm not an actual doctor, but they may not be able to firmly diagnose what exactly it is with swelling and the sheer number of bones and tand because of that the cast is a precaution. I think the thing you really have to worry about with feet are Lisfranc injuries.
https://orthoinfo.aaos.org/en/diseases--conditions/lisfranc-midfoot-injury/