The trusted 3rd party in this case is actually multiple 3rd parties. There's several options for trusted timestamping just like there's multiple trusted root CAs for SSL. Since the timestamping service is free and public, anyone can use it to sign anything, even self-signed certificates. There's no mechanism to deny access, at least for this portion.

There's always a risk the root CAs all collude and refuse to give out certificates to people they don't like, but at least so far this hasn't been a problem. I don't have a better solution unfortunately. If we could have a 100% decentralized signing scheme that would be ideal, but I have no idea how you would build such a thing without identity verification and some inherit trust in the system

Another option is to allow otherwise-valid signatures after expiration. It's generally still possible to check them.

If it's anything like how Windows does it, you would still be able to override it. It just gives you a scary warning and hides the option unless you click "more info" or something.