I agree with your premise that password resets and system emails for a typical app shouldn't be HTML, but for you I really think they should be. It's your whole product and a perfect opportunity. If I get a really sharp clean welcome email or password reset, etc... I'm much more likely subconsciously associate your app with beautiful emails.
I completely agree. These days there's very little wrong with sending HTML-based transactional email provided you've covered your bases on all other potential flags and send as multipart with a plaintext component. At PostageApp many clients have amazing inbox delivery with HTML transactional, and the benefits - improved tracking, better funnel direction etc. - outweigh the minor delivery drawbacks in many cases.
Frankly, many who send 'plaintext' transactional in fact end up sending as HTML these days in order to facilitate open tracking from embedded images, so aren't gaining much beyond avoiding the minor issues like 'HTML_IMAGE_RATIO' etc.
edit Apparently the MailRox invite email _is_ an HTML email for the exact reasons outlined above. I can see no reason why you wouldn't want to add some visual sparkle to this based on that fact. Incidentally, you're sending without a plaintext component which can cause delivery problems at some ISPs.
You're right, I'm really on the fence with this, it's a hard one. I'm going to look into getting a light-weight HTML email for the system notifications. If the right balance can be struck I'll go for HTML.
Edit: When I say HTML I mean well designed (boxes, colors and logos). At the moment, like tomwalsham said, its just some <p> tags.
Just to add my voice to the thread above—I also thought it was odd to get a plain-jane invite email. The overall idea of the app is really enticing to me though because I really hate coding up emails using the old-school tables, font-face, etc.