The battery doors are uniformly fragile on almost all digital cameras;
the Nikons you mention are perhaps a little bit worse than average. I
have experience with the 3100; with careful use it can be made to hold
up. But as you mention, the stupidity is that the door is not designed
to be easily replaced. I've also noted flimsy battery doors all the way
up to my D80.

Your 5000 battery experience is atypical. I've had good performance
with Nikon battery packs back to the CoolPix 995. In fact the battery
that came with mine years back is still fine. Are you buying genuine
Nikon batteries?