Interesting choices - but don't they mostly illustrate the opposite point?
Star Wars - almost all damage suffered is basically cosmetic and healed extremely quickly. Even Luke getting his hand chopped off is essentially cosmetic as he's good as new soon after (extended rest?)
Lord of The Rings - Again beaten up bruised battered, but cosmetic unless the character actually dies (or suffers from a disease/affliction such as when Frodo gets stabbed).
Rocky - Pretty much the embodiment of cinematic healing surges in action! Teeth lost? eye swolen shut? Rub some spit on it, cut it and move on!
Robocop - haven't actually seen this one (treasonous I know) but isn't the only scene where the hero gets beaten to near death (death?) essentially a cut scene used as an excuse to introduce the new form and therefore cinimatic license?
Overall it depends on how silly of an action movie you may way. Likewise for games.
Robocop he is dead, they insert some of his organs and mind into the robot body.
Star Wars...Vader (see RoboCop), but he is changed from the incident. Luke's hand wasnt just an overnight thing. Sure he could use it, but had to train again. For overnight they could have just grew him a clone and used spare parts for either of them now couldn't they? Also most people seen were high on midichlorians that were the life force bacteria of the universe so akin to magic to heal them faster.
Rocky, he was in a coma. I call that pretty much NOT overnight healing.
LotR, the reason they healed for the most part quickly was due to the use of magic, not just sleeping. Frodo woke up to find Sam and the others in Rivendell, and magic had been used to heal him. Denethor didnt wait a night for Faramir to get better, he was about to burn him alive, and Faramir didnt just jump back into action the next day.
Théoden was being controlled by magic and within minutes was cured by magic, but at Helms Deep he was quickly taken away after being injured in his token appearance in the fight as king and didn't just rush back to battle later, but had to heal after returning to Rohan, as well Théodred just up at died rather than sleep a night and get back up. Several arrows is all it took to take out Boromir.
Mostly LotR revolved a great deal around healing magic rather than being really injured out in the field away from plenty of healing magic. The only person really injured and not die was Frodo, because he was rushed to be healed by magic. The Hobbit had plenty dying or out of commission due to injury lasting longer than just a night's rest.
So again, it is the type of cinematic you are trying to present. Also how long do you want to see the hero laying in bed resting, even if he is in an action movie? Isnt it about the action rather than the time it takes for them to heal, so you skip past that rather than show the days of time it takes.
I could go with Hard to Kill, Bourne Identity, and Wolverine also, and Wolverine has supernatural healing, but even he carried more than just superficial damage from it.
There are MANY stories where the hero is out of commission for longer than a night. Even anime has the heroes down for longer than a single day with all the things they do.
Again that plays an important part int he stories some want to tell, so the game changed to move to a different type of story, which shuts out those others, or you have to explain somehow that it happened some other way than it played out, or just use magic healing.
Some mechanics just seem to prevent certain types of stories, based on them removing some elements from being there, such as healing. The story of a character overcoming his injury to get better is gone when the injury is pretty much ignored through "strange" healing.