You're right, this doesn't solve 100% of the problem. If I could solve 100% I'd be creating a startup...
Cookies are remarkably sensitive, but they can be far more easily rotated. I can make sure that every cookie is rotated transparently every day or so and leave that running as a sensible background precaution. If we had infrastructure that let us renew our TLS keys every 24 hours or so, this wouldn't be such a big deal (it would still be a big deal, but not quite as bad as it is today). But TLS keys have an expiry of usually years.
Cookies are remarkably sensitive, but they can be far more easily rotated. I can make sure that every cookie is rotated transparently every day or so and leave that running as a sensible background precaution. If we had infrastructure that let us renew our TLS keys every 24 hours or so, this wouldn't be such a big deal (it would still be a big deal, but not quite as bad as it is today). But TLS keys have an expiry of usually years.