To fix or not to fix - that is the question

In what way is the wheel fucked?

Assuming your rim/tire/etc is fine, why not get a new fixed hub and get your LBS (or any good wheel builder) to replace the hub on the old wheel (plus any other new stuff needed) ?

I've got one working bike of each kind and only use the geared bike when the fixed breaks. When I'm forced to use the geared bike I don't particularly like it.

never gonna be worth changing the hub over at the shop for a well beaten wheel off a basic 501 bike.

Better to purchase a new wheel separate.