The thing is that with the way the armor upgrade system works, even though the Catholic halb militia could get partial plate, they only get something like +3 to their armour at the end, not 7 or 8. This means that they still get shot up like nothing.

Halbs could be viable at bridge crossings and can likely stop an early massed cavalry assault but would get shot a lot. Later mongol stacks also come with trebs and rockets which would do a number on the halb formations.