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 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, etc. yet. These are pretty advanced concepts.