Informal is fine. The important thing is to do user testing in an ongoing way, not just once. Without a feedback loop it's quite surprising how quickly development priorities diverge from what's really important.
Members of all the Rust subteams are constantly involved in guiding new users through the language. Come to any Boston Rust meetup and you'll find Niko Matsakis giving one-on-one help to people taking their first steps. And it's not just feedback from people in major tech hubs; Brian Anderson and Alex Crichton just got back from mentoring new users at Hack Illinois in Urbana. They go to great lengths to remain plugged-in like this.
We are always constantly trying to listen to people and get feedback; for example, it's one of the reasons I pay such close attention to these threads!
There's always room for improvement, but iterating in this way is defintely a core value.
Depending on what group you're trying to attract or improve the experience with, you could potentially setup contracts with the level of person you would like to deal with and pay them to implement something in rust while you monitor their progress & with full access to their work and what they're doing.
The issue is, of course, that the more you focus on specific tasks the more your language becomes "designed for" those tasks, and the language becomes less general. The language already went through some of this with Servo - the DOM would be much easier to implement with an object-oriented language, but that wouldn't fit in well with the rest of Rust and would significantly raise complexity.
That is a concern but the other risk is by not doing this the language progresses in areas people happen to currently use it, which will be skewed by what it's already good at. You can then end up never improving for those cases it's weakest. This covers types of programs but also experience levels and histories of the programmers themselves.
You are right however that you need to carefully pick the tasks to fit with the original aims of the language.
Perhaps a good way of phrasing this is "why aren't X people using rust for Y?".