Yes, this actually would be possible. To do what you asked, specifically, you would create 2-of-3 multisig transaction addresses where the third key is owned by a third party (likely web-based) service. When you lose access to one of your two private keys, you could use this service to recover your funds at whatever predetermined rate you chose. Such a service could require a login, or not, depending on the security you desire.
Why add in a web-based service since it is not necessary in theory? Does it have something to do with the code lacking awareness of the blockchain? Are the core code modifications necessary to remedy this too difficult?
In my view, there should be a plan where txns with time-dependent spending limits without help from a third-party service become possible at some point. Maybe this is too tough to achieve right now, but it seems like a cleaner, more convenient, and intuitive solution to me. Time-dependent spending limits have such prevalence in consumer banking that I think people will be uncomfortable without them.
Third party service providers can cause lots of problems. Many people are already quite uncomfortable with them. "Don't lose two things at once" strategies also make things quite complicated. People get worried by stuff that is complicated. Who wants to spend the mental energy to deal with multiple methods of authentication simultaneously? I'm not saying I don't see value-added in these proposals, it is just that they do not seem like permanent, first-best solutions to me.
Should we view these proposals as temporary fixes?