And we've learned over the years working on Inky (http://inky.com) that users simply, positively, absolutely will not accept a mail client that's not MVP in all the expected areas. If people can't use your mail client as their primary mail client, they're not going to use it at all. This makes delivering incremental improvements like turning the inbox into a task list very difficult -- impossible, in my view, which is why we've created our own complete client stack.
Thats been our not-so-secret strategy from the beginning. It allows the user to slowly onboard to your product instead of making a one time "do I want to switch over my email?" type of decision which is obviously much harder.
What is your business model for it? Since it's free, are you parsing all the mail and providing data services to interested companies looking to mine information?
I'm not sure what you mean about using the front-end without the back-end, but Inky's an IMAP/POP client like any other; it just stores your settings in the cloud. (If you mean "can I use it without storing my settings in the cloud", the answer is currently no... at least, not yet.)
We are not parsing the mail and mining data from it, nor do we plan to. We're looking at various non-privacy-invading ways to make money but we need more real-world data to see what makes the most sense.
I don't necessarily know how well you are protecting them, or if your admins are able to copy my password. Even if you encrypt it, who's to say how well? What if you DB leaks, and my credentials are in the hands of the "bad guys".
It's not fundamentally terrible, but it increases the attack vector..
We're going to add this as a FAQ on the site with the next rev.
We're hoping to reduce the need for emails and at the moment are trying to be that second tool after email.
A 'twitter for teams' is a way someone described Task Messenger to me recently.