I can't speak for the 737 specifically, but if the fuse plugs melt, I believe the tires will go flat to prevent them from blowing out. I would not taxi after that.

As for not setting the parking brakes unless pax have to evacuate. That is to prevent hot brakes from melting closed, or applied, and to help prevent them from catching fire.

I have never seen the fuzes go, but I have seen hot brakes that melted closed. Took maint a week to get them fixed.