I'll cast my 'yes' vote for this suggestion. As someone who is experienced in IT/technical support in a former life (in a manner of speaking), and has helped others as a gamer, I don't think its any stretch to say that not all gamers are necessarily technically savvy. And I know via different games and betas I've participated in, some ask for external emails with crash dumps/dxdiag/screenshots etc etc via email, which isn't the most elegant approach by any means, and especially not for those who aren't as comfortable or savvy in having to do so.
If the game client has a means to instantly capture all needed files (which should be generated to a specific local drive location anyway), and pops up a dialogue window for the player to provide detailed feedback alongside that to explain what they were doing and what happened at the time it occured, that would be the ideal. And then, as stated here, even then when a crash isn't involved, its still more convenient to have an in-game reporting dialogue tool to be able to capture information and submit on the fly.