It appears that a Mega Man first-person shooter was in the works a few years ago, but was unfortunately canned.
According to Polygon, the game was codenamed "Maverick Hunter" and was under development in 2010 at the hands of Armature. For those who don't know, this studio was founded by the brilliant minds that brought us Metroid Prime. A match made in heaven? Yeah, I would have thought so.
According to the outlet, “the game would have stayed true to core Mega Man X gameplay concepts, re-imagining his X-Buster arm cannon, his dash and his ability to appropriate the special powers of his fallen enemies. Platforming elements, including X's wall jump, and classic Mega Man X characters would have been re-imagined in new ways.”
"Maverick Hunter" was scrapped just before Keiji Inafune parted ways with Capcom. Interestingly enough, it was supposed to be the first part in a trilogy of games where, in the concluding title, "the player would assume control of Zero, forced to destroy a Mega Man who had grown incredibly powerful and infinitely intelligent over the course of two games.”
I can't be the only one extremely sad that this project never saw the light of day. Feel free to lament its cancellation in the comments below.