How modern computing quietly depends on this constantly-maintained layer of trust infrastructure
Well, to be more specific, "modern internet/web". Most of the applications that ran on a Windows XP computers still run on a Windows XP computer without hiccups, unless they do a lot of network connectivity for the functionality.
And no one can even give a concrete answer why root certificates need expiration dates. It's just because reasons.
IMO the whole PKI thing is a terrible idea to begin with. It would make much more sense to tie the trust in TLS to DNS somehow, since the certificates themselves depend on domains anyway. Then you would only have a single root of trust, and that would be your DNS provider (or the root servers). And nothing will expire ever again.