Those issues are partially addressed with "identity based encryption," but IBE always has a "backdoor" because there is a party that issues the users' private keys (and hence can always read a users' messages). On the other hand IBE does allow you to "just send" an email to someone because the public keys are just the "identities" (e.g. email addresses) combined with a single master public key. Key management is not as much of a problem because of how keys are generated. IBE does have some users, but as you said it is mostly business/organizational use.
If you could actually solve the deeper problem of the sender being able to find the correct certificate to use for the recipient(s), then the lifetime could and should be as short as possible, as in days not years. The recipient can decrypt the message forever, as long as they continue to possess the private key, even if the associated certificate expires. Short-lived certificates are the only effective mechanism for dealing with key theft and mis-issuance that works at scale.
Let's Encrypt is bringing the duration of certs down not up. I believe their goal is 30 minutes validity.
This is mandated by the CA/Browser Forum, which, as the name implies, is related to browsers. It says nothing about e-mail clients. In its Extended Key Usage filed (RFC 5280 § 4.2.1.12) a certificate could not have server or client authentication, but have email protection as an allowed use.
Edit: there is an RFC for "Extensions to Automatic Certificate Management Environment for End-User S/MIME Certificates"
The most aggressive plans (not Let's Encrypt's specifically) target 7 day validities.
If the cert lifetime is 5 years, Bill installs "just the first one" manually, solemnly swearing they will automate next time, and in five years nobody even knows who Bill was, Bill left three years ago. How do we replace the certificate?
If the cert lifetime is 2 years. Bill is still there or maybe somebody on the team still knows Bill's email address, but most likely the decision is taken to "just do it manually once because it's urgent" and we just recurse. This would have been the "obvious" choice when ISRG lit up Let's Encrypt.
But because the cert lifetime was 90 days, Bill gets told it's expiring at about the same time he's about to shove that "Actually automate certificates" work onto the back burner. Oh yeah, right, we should actually do that.
Now, it may be that at a startup that "Automation" is initially "Put it on Natalie the intern's TODO list every Monday" but by week six Natalie has learned about cron, or Windows event scheduling, or a dozen other ways to make stuff you always do regularly happen without actual work. Today I expect her LLM will tell her how to do it.
And Natalie is going to discover that some "permanent" solutions are more permanent than others, that you want monitoring and so on. But because Let's Encrypt is so popular unless you're doing something pretty esoteric you won't even be the first person to ask about it this month.