>> I can prove my identity on my computer and have it be valid for all apps for a period of time?
2 reasons really.
1) how to know the computer is honest?
2) how to trust the "one true login to rule them all".
Let's say you 2fa the PC at the start of the day. Then anyone with access to the PC, including remote users, can get access to all services you subscribe to. That makes your machine a very juicy target. And if compromised the penalty for failure is large.
2) all the services you use need to trust the SSO provider. Which makes them an even juicier target. Incidentally Okta -is- in this space, and does what you are asking for, and has been compromised a couple times.
Or to sum up, security is proportional to inconvenience. Improving security makes things less convenient, and vice versa.