A quick glance at the page doesn't tell me if this thing processes my E-mail online, or locally, and what data gets shared where and with whom.
On the other hand, the evidence seems to suggest that people will give up nearly any amount of privacy for a little convenience, so everyone but the sort of people who read HN will probably love it if it works well enough.
So, I need to move my email to be hosted on your servers? Because if not, the correct way to the describe what you're doing is: "email is sent to our servers" which is the opposite of: "Your emails aren't sent anywhere".
Do you manage your own servers? Is the answer really, "your email is sent to virtual servers we lease from Amazon" for example?
It's not that trusting (yet another) party with full access to every email is necessarily a deal breaker - but every additional service and ops team that gain access is another potential human error added, that could lead to compromise.
Even compromise of something as trivial as ones email address: I currently get almost all spam to the addresses I used to sign up for Adobe, LinkedIn and Dropbox before they each got hacked in turn.
The only sensible assumption about a new service is that it will be compromised at some point - it's important to be able to evaluate the risks involved. (So you not storing email in perpetuity is good to know. One does wonder how much data might be gleaned from getting a copy of a neural network trained on my personal correspondence for a decade though).
They are sent to your server. Which means they are being sent somewhere.
Seriously? Something tells me you picked the wrong crowd to be dissembling with....
So, they are sent to at least three different entities: your ISP, your hosting provider and you.