Tony Stark's Iron Man armor in the Marvel Cinematic Universe underwent various upgrades since the character first appeared in 2008's Iron Man. Thankfully, one of those upgrades wasn't to Stark's Bleeding Edge armor - one of the grossest and coolest armors Iron Man has worn in the comics.
Iron Man's Bleeding Edge Armor first appeared in The Invincible Iron Man #25 by Matt Fraction and Ryan Meinerding. The armor isn't external like Tony's past suits, it's internal. It's stored inside Stark's body using nanotechnology to form a suit from inside of him. Stark essentially made himself transhuman, commanding the armor mentally. It would spawn from his body and mold onto his skin. There was no need to carry a suit around, as he could activate it whenever he needed it.
Stark's Bleeding Edge armor is extremely powerful. It could self-repair when damaged, was practically invulnerable, and could be restored in seconds when destroyed. Stark literally made the suit a part of his body. His transformation when wearing the suit was incredibly cool, but also disgustingly gross. You can see the nanites take over and graft the suit onto his body.
It is pretty easy to see why Robert Downey Jr. didn't sport an exact version of the armor during his time as Iron Man in the MCU. It simply was too gross to include in its comic form. The Bleeding Edge armor would have traumatized kids and watchers alike. The transformation is neat and cutting edge, but there was no real reason to have Tony Stark go full transhuman. It would be unnecessary body horror, and just wouldn't fit the tone of the films. Instead, giving him an advanced suit, like the Mark LXXXV, that could be summoned when needed was a much better choice.
The Bleeding Edge armor lasted a couple of years before Stark retired from being Iron Man in 2012. In the Long Way Down arc, Tony undergoes a surgical procedure that removes the Bleeding Edge technology from his body - making him fully human once again. Most recently, Stark's armor became even more disturbing.
It is very Tony Stark of him to design a suit that was stored and enabled from his own body. Stark is a genius who loves to take risks. By implementing the Bleeding Edge armor into his own body, he was doing what he does best, testing his own limits in order to be a better hero. It was a noble move, but we're glad it stayed in the comics - even if the Bleeding Armor was one of the coolest suits Iron Man has ever worn. His MCU suit-ups should be epic, not disgusting.