The robot thing is so ingrained that it even pops up in places you wouldn't have expected, given the premise (I'm looking at you, Wizard Barristers, where the "Perry Mason with magic" premise and things like animation for most of an episode were all sacrificed for a CGI mech fight climax).
Heck, even Pokemon has them, courtesy of Team Rocket (though needless to say they're anything but awe-inspiring). My point is, they're that ubiquitous. If an anime series goes on long enough, and has a reasonably sci-fi/fantasy-based setting, chances are it WILL involve giant mechas at some point.