Metal sheet inside bottom bracket on frame: can I remove it?
Based on your description, its some kind of "cover" that would stop water dripping down the seat tube from sitting on the BB axle.

Seat tubes are notorious for leaking, mostly because the slot at the back of the seat post is an entry point for water, which then weeps downward by gravity and eventually drops through the weld breathing hole between the BB tube and the bottom of the seat tube.

In theory water should continue through and drip out the drain hole at the bottom of the BB, but some bikes don't have that so water collects.

On the other hand some frames have ridiculously oversized cutouts like this which allow a lot of water to spray up off the front wheel:



So your metal shield could be doing the same job for water from the road.  Above picture shows a white waxy plastic liner.

So in theory your modern BB cartridge will have a shield purely because it IS a cartridge already and is much more resistant to moisture.