Which is yet another chore. And it doesn’t add any security. A certificate expired yesterday proves I am who I am just as much as it did yesterday. As long as the validity length is shorter than how long it would take somebody to work out the private key from the public key, it is fine.
Right. It's the same debate about how long authorization cookies or tokens should last. At one point in time--only one--authentication was performed in a provable enough manner that the certificate was issued. After that--it could be seconds, hours, days, years, or never--that assumption could become invalid.