Came across this nifty idea earlier in the week. I had a feature I'd been looking forward to building for months, then another probably more important feature popped up. Important, but probably not that in demand.
This 'important' feature didn't need any new database rows or anything like that, it was just using existing data and was something I could do very quickly from the console. I decided to simply add a new button to the dashboard, which was actually a mailto link to one of our email addresses (along with a subject line and body pre-loaded with an explanation ).
I quite like this approach as it doesn't mean a rushed UI design and also serves as a bit of an experiment. Maybe this feature is not actually needed and I'm just assuming things etc.
I think if you did this lots, customers would become a bit fed up. But 1 out of any 10 features being an email request seems reasonable. Also, I should mention we're not freemium, all customers pay (unless they're in a trial). I can imagine this approach being problematic if you run a really large app or an app with lots of free users.