It's a compromise, if it's too much hassle the average person will just (re)use weak passwords which is probably worse.
Keepass has an auto-type feature which can be used in place of browser integration. It's not as good, but it's preferable to the mess that we're seeing with LastPass.
The longer-term answer is going to be the use of a trusted central authentication service, with federated access to downstream services. A lot of places will currently accept Facebook or Google auth, which is a start. That way you can enforce strong authentication via a single username/password with 2-factor protection, and you don't have to have individual passwords for each service you use. Ideally we would have something like the Danish NemID but the average Daily Mail reading moron would throw a fit if the government decided to get into the authentication game.