I don't care what JMAP wants to do for me as long as it's not actually available to me. IMAP supports downloading headers too -- that doesn't mean everyone uses IMAP 24/7. The IMAP + local synced maildir use case is extremely common and there's no reason JMAP can't do it better.
I merely suggest that starting by making small shims for interoperability would encourage protocol adoption so that when clients arise they'll be in a position to be successful out of the gate.
They are providing an open source server implementation, which is a great way to increase adoption. Adding support to widely used open source mail clients is also a great option, but I doubt usage of mutt is anywhere near high enough to provide a good return on investment.
Implementing in the default mail client on Ubuntu might be worth it, or maybe the most popular open source web mail client that exists could be worth it. Ideally though they need adoption in something like Outlook, Gmail, Apple Mail/iCloud, etc, but these are all closed source so a) impossible to do without support from the vendor, and b) of limited use to increasing the community of JMAP implementors.