Security keys are supported on Google and Facebook on (almost) all browser/devices. Almost means you still need to be a bit careful when you buy the key to check exactly the support, but you'll find the right combination that works for you. If you want some extra websites, you also have Twitter, Dropbox, Github, etc.
This said, I personally wouldn't want to enable my security keys on too many websites, because loosing or breaking a key it's a major pain. I much prefer to use oauth and delegate authentication to Google or Facebook, and keep these two highly protected.
But the real value is for the most critical logins, such as to Google, or similar, where a breach would be tremendously harmful to you.
Edit: here https://lastpass.com/support.php?cmd=showfaq&id=8126
U2F works with dashlane I think?
tl;dr: You can use the yubikey to replace google authenticator wherever you're using standard TOTP codes.