I've seen it. Websites are pretty inconsistent about the flow but I've had a few just try to install a passkey when I log in (amazon does it. Paypal seems to do it but only try to use it on the same browser it was installed on, even if it's synced through a password manager, just to be different. The more reasonably ones have a 'log in with passkey' button but this isn't universal. Microsoft seems to just nag the user on login periodically in their classic 'Yes/Ask me again later' style of 'consent'). You can, if you're paying attention, avoid it actually happening, but the average user isn't going to notice until they suddenly can't log in because they're on a different device. You can see some advocates are pretty vocal about making them mandatory as well.

I feel like dozens of sites constantly nag me about this. The best ones at least save a cookie to note I'm not interested, such as GitHub.

Every time I login to certain sites (like my health insurance, for one) I get a passkey prompt (system dialog) with no way to keyboard-dismiss, so I'm forced to move my hand over to the mouse and figure out which of three poorly-named buttons to press to get on with the login and ignore the passkey.

It's a minor inconvenience, but happens so regularly I hate it. It also stops the login flow until I dismiss the prompt, which is also annoying as I could've already gotten to the page I wanted to get to in the time it took to dismiss the dialog.

You must not use Outlook