Default [Q] Incoming call does not trigger dialer screen

I'm having this issue where the phone doesn't react properly to an incoming call (stock ROM, unrooted).

The phone rings, but the dialer screen with the controls to answer the call does not come up. It doesn't help if the screen is already on, I'm just staring at my home screen while it rings. There's also no call icon in the notification bar. When the caller hangs up, I immediately get a missed call notification.

Rebooting the phone solves the problem for a while, but then it comes back. I tried reverting to the stock dialer with no luck. I'm thinking of reverting to the stock launcher as well, but I'm not sure it has anything to do with it. Other than that I'm running out of ideas.

I've searched the web and it looks like people are experiencing all sorts of variations on this problem, but not the exact same thing, and in any case I haven't seen anyone post a tested workaround.

Has anyone encountered something like this and maybe knows of a solution?