Well all the E-mail clients i have used, INCLUDING Thunderbird, let me dowload nad erase from server (or not now that someone reminded me) the folders I stored in with T-Bird were all local.
But once I got into more serious use of the internet. I stopped using client mail. I hear folks say "Crappy web mail" but I've not seen that. The only advantage I've seen to client mail is I can "hit" the server, then go offline.
Back in Dial up days, that was good. but with modern always there internet, I use web.
And I go all the way back to a program called NET TAMER.. HINT, not a windows program. Older than that.