The most heavily loaded Mail.app I seem to have is one with two MS Exchange accounts, iCloud, a couple of IMAP accounts and a single POP account. I generally archive everything older than ~10 months out of my inbox leaving a combined 43k messages in that virtual inbox 'group'. Maybe people with larger message stores trigger some programming fault?
It's strange because I like a lot of what Mail.app does—it's simple, no bells and whistles—but the search experience, etc. just ruins it entirely.
But god, these bugs. Somwhere down the line it became strangely slow. It's constantly displaying false values on how many emails it is about to fetch. And I accidentally deleted emails on more than one occasion without having a clue on how that happened.
In the end I went with Mailmate and I’m extremely happy with it.
https://en.wikipedia.org/wiki/Mutt_(email_client)
Depends on your definition of 'desktop', of course ;)
Mail not being able to properly find an exact string match correctly means I had to give up and just use GMail in Chrome and on iOS. Once GMail on iOS added IMAP and SMTP, I never needed to go back.