That is the wrong assumption. They don't need to compete with anyone. As a commercial software they only need to make enough money to survive for their own good. As a non-commercial software they don't even need money, just enough attention to stay useable. And in both those camps there are still many members alive.
Non-commercial doesn't really matter to the thread.
Commercially, you see the occasional upstart, but inevitably they die after a few years. I used Airmail for a while but they just stagnated (they barely kept up with Gmail and struggled with Exchange) so I had to drop them.
The market for commercial desktop email clients is super-small: the intersection of the already-niche subgroups of people who will pay for email clients, people who will pay for desktop software, and people who will pay for already-commoditized software. The effort is simply not worth the small rewards, particularly compared to the impact one could have by building on existing commodity clients.