What I worry about with OpenID Connect on the open internet (as opposed to OpenID Connect used in a corporate setting, or to provide single sign-on solutions for specific partnered services) is how it almost always results in a service asking you to use Google or Facebook to authenticate, with huge coloured buttons, followed by a tiny de-emphasized grey link where you can sign up using email and a password.
Is this something we can prevent?
As a site developer, it is your job to figure out what buttons your user demographic will use. If it is all facebook / google, then provide those, and most of these sites know providing more obscure options only confuses their potential users.
What we're working on (we will definitely post about it) is basically OIDC with a nicer UX, where the user enters their email, the domain is parsed out, discovery (of OIDC or whatever other protocol) is done, and the user is redirected to either their provider, if found, or to a default method of authentication (currently a link sent over email) to log in.
I'd much rather see the use of password managers become more common, or even better, stimulate user-friendly two-factor authentication standards such as FIDO U2F.