I assume there are benefits -- I guess one I can think of off the top of my head is that your email is accessible offline. Surely there are others though
Having your mails accessible offline is more of a protocol question.
1. Unified single entry-point into all my email accounts. I I can search through all of them even while keeping them isolated from each other (to allow searching individually).
2. Latency: when I want to open an email it does not require a 500ms delay, as in gmail, roundcube, whatever. You may think this is not a problem, but if you perform a search and want to quickly open all 15 of the results, that latency adds up quickly.
3. Slicker UI, in most cases. Especially in searching (which is different from "filtering"). UI for adding rules to kill based on patterns is a lot easier than gmail, for example.
To be honest though, looking at my points above, it basically comes down to "searching is better on local client".
Why are you implying I only use one provider?
- I can search all of my emails at once.
- I don't need to worry that much about account management.