@lggr, this forum has an interesting mix of end-users wanting to fix their own computers and web site administrators wanting to improve/maintain compatibility of their web sites. This solution has already helped a number of end-users who were actively trying to diagnose and fix their own problems accessing web sites.
I hope we'll find better solutions that work for all web sites, but it's also possible that Let's Encrypt certificates simply won't be able to support certain clients in the future, especially client platforms that are no longer supported by their vendors. The web PKI model does depend on having software vendors maintain root certificate stores over time, which also means eventually pushing out new roots to replace old ones as the old roots go out of use.
Unfortunately, that problem isn't specific to Let's Encrypt in any way. All root certificates expire and are eventually withdrawn from use at some point. As @jsha pointed out in another thread, there seems to be an industry-wide mismatch or failure on this point; unfortunately, Let's Encrypt users are those happening to experience this at this moment, but users of other CAs will also experience it (or have already experienced it) at other times.
It's also a concern that so many people continue to use software that no longer receives security updates. I think @jsha's post suggested laying blame more with software (and sometimes hardware) vendors than with end users, but however we want to explain the problem, it's a really concerning issue; it's one of the ways that bot herders have been able to incorporate so many devices into their botnets. The increased use of cryptography makes this problem more directly visible because security updates for cryptographic systems are often not backwards-compatible.