In my opinion, the downside to MimbleWimble / grin is that it's an interactive protocol. Meaning I can't just give someone my address, go offline and they can send me Bitcoin at any time.

Especially if we talk about larger sums that I want to hold in cold storage or if I use a mobile wallet that goes to sleep after a few minutes in the background.

The probably biggest reason 'Why Bitcoin addresses exist' and BTC doesn't use grin's (or a similar) model is that Bitcoin is much older and when satoshi came up with it, nobody was thinking about address reuse and deeply about privacy yet. Bitcoin was pseudonymous from the start and it was known not to be perfect in terms of privacy. But these are pretty advanced concepts that were always meant to be tackled later on (i.e. now).

You could argue that Lightning gives Bitcoin the feature you are looking for: anonymous, but interactive payments, without addresses.

Maybe you have some Bitcoin Layer 1 privacy ideas or papers that I missed and I'd be glad if you would post them here: [Megathread] Bitcoin Layer 1 Privacy - concepts, ideas, research, discussion