Yes, the MCU has embraced that stuff from the beginning, but I was just talking about super hero movies in general, which seemed to make a point of avoiding the bigger, more SFF stuff for a while after Batman Begins came out. Thor, the first Avengers, and the first Guardians of the Galaxy were some of the first adaptations to really go all in on that kind of stuff.
I don't think
Batman Begins has anything to do with it. If you look at comics-based screen universes in general, they have a pattern of starting out doing more grounded stuff to appeal more to general viewers and cautious executives, then gradually easing into the more fanciful stuff from the comics. The DC Animated Universe started with the relatively naturalistic
Batman: The Animated Series (which had robots and AIs and shapeshifters and such, but no aliens or space travel and no magic save one episode), then waited until
Superman and
Justice League to bring in the wilder stuff.
Smallville started out aggressively minimizing its comic-book elements and trying to be more of a pseudo-supernatural teen drama in the vein of
Roswell, but as it went on, it became more and more like the comics. The Arrowverse started with the gritty, street-level
Arrow, with no superpowers or other major fantasy elements, then brought in superhumans with
The Flash, time travel with
Legends of Tomorrow, aliens in
Supergirl, and eventually full-on magic and fantasy. So similarly, the MCU started with
Iron Man and then worked its way up to more fanciful stuff. Same with the MCU on TV --
Agents of SHIELD began as an ABC-friendly show about unpowered government agents investigating weird phenomena, a proven TV procedural formula, then gradually started adding superhumans to its core cast and embracing increasingly far-out premises as it went.
Although I suppose the Batman film series itself is an exception to that pattern, since the modern era of Batman films started with the fairly fanciful Burton films and the even more fanciful Schumacher films, then gave way to the gritty naturalism of the Nolan films. So it's not a perfect theory.