It was Paul Levitz who put the kibosh on such things. After Bill Jemas and Joe Quesada insulted DC Comics rather foully in the national media, the edict at DC Comics was that no crossover between the two publishers could be entertained until both people had been fired by MArvel.
And the last time Brian Bendis raised the matter for a proposed Batman/Daredevil crossover, it was DC's Bob Wayne that indicated that Marvel was only halfway there in that regard.
It's a different regime at DC Comics now, but crossovers with Marvel are still off the table – though they are fine for Boom and IDW, it seems.
Well here's an example of "look what you could have won." Joss Whedon told Marvel.com that "I had had a very big concept years ago that I desperately wanted to do which actually was a crossover with Captain America and Jenny Sparks from the Authority. It was about Captain America early in his career learning about the history of America, what's good and bad about how this country was formed and how that's reflected in Europe and so he didn't have this jingoistic bad view of Europe and so the point that's made in the little piece that we do here is how I wanted to end that which is him realizing what his purpose is and it's not you know to hit people."
DC Comics don't even publish The Authority these days. But Whedon has taken that concept and turned it into his Captain America story for the 75th anniversary in Captain America: Sam Wilson #7, with John Cassaday.
Taking about the Avengers movies, he seems to equate Tony Stark with another figure big in the media at the moment. "I wanted to say about how people have changed and we've gone through a world that values Steve Rogers to a world that values Tony Stark. [Tony is] rich, he's obnoxious, and he thinks he can solve all the problems and will die if people stop paying attention to him. I mean, don't get me wrong, Tony's a dream to write and Robert [Downey Jr.'s] amazing at it, but Cap contains a kind of assertive squareness that I think we legitimately missed."
Well, I suppose Tony does have Stark Tower….