Sneak in burglaries are relatively common in many areas of the UK, including the nice ones. Several of my colleagues have had handbags, cars, laptops, phones, money etc stolen by people walking into their unlocked houses. And these are the ones that live in nice, Mumsnet approved, areas of the city. So standard police advice is to lock your doors, even when in the house.
But OP, your DP sounds like a controlling arse. I bet that he manages to take his phone and his wallet when he leaves the house, so why not his keys?
There's no way I would be jumping up to let him in if you're in the middle of cooking, hanging curtains, in the bathroom etc. If he has to wait on the doorstep, it will give him time to come up with ways he can remember to take a key with him.
It's not about not helping him, it's about him being a grown up. Remembering to take a key is something that most people get to grips with during their first year at secondary school. He's had over a decade and he's still not mastered it. WTF?