Are these studs intended to hold a drywall ceiling, or just for foam insulation?
It's not called "bridging," it's called "strapping."  It is intended for drywall or some other ceiling material.

It doesn't look to be well-fastened, by the way.

You DO want to hang drywall from those strips instead of the joists.  They help to even out the inconsistencies of the bottom of the joists, also making it easier to orient the long edge of the drywall perpendicular to the joists.