Some broken foots do get a cast and some do not.
Whether or not your broken foot gets a cast will depend on how bad the broken foot is.
If the broken foot has a slight fracture then it may not need a cast but if the broken foot is worse and has a larger fracture then it will likely need a cast.
A broken foot or other broken bones need to be immobilized so that the bone ends can knit back together.
But for tiny fractures in the foot they may be able to heal and grow back together on their own without a cast as long as you keep a lot of weight off your foot while the broken foot heals.
I once had a small fracture when I broke my foot and they didn't cast it and instead just said to keep my weight off of it and it should heal within a few weeks and it did.
Then about 5 years later I broke my other foot more badly and they cast it to allow it to heal properly.
The broken foot took 4 weeks to heal since it was a larger fracture.
Minor foot fractures usually only need a removable brace, boot or shoe with a stiff sole.
And a fractured toe is usually taped to a neighboring toe, with a piece of gauze between them.