But the realism of D&D worlds is not the same realism as MCU. In the MCU you can be a 0 level nobody(Peter Parker) and get bit by a magic spider and instantly be stronger than the Tarrasque. The Tarrasque by the lifting rules can only lift 7200 pounds. A medium creature with a 30 strength can lift 900 pounds. Double it to 1800 for large, to 3600 for huge, and max it out at 7200 for gargantuan. Spiderman can lift 20000+ pounds. Add in Spiderman's spider sense and agility, and he's better than a 20th level fighter. All with no experience points gained.
MCU and D&D worlds might have an equal amount of realism, but it's a different sort.
Like
@Vaalingrade said, that's an issue of the encumbrance rules. Translate Spiderman to 5e and he has a max strength of 30, so he wouldn't be lifting 20k lbs in any D&D universe under the current rules.
However, there are plenty of examples of "super powered" individuals in D&D.
Midnight (from the Time of Troubles) suddenly gained the power of a goddess. Her fighter-protector who was from a cursed lycanthropic bloodline.
Pretty much anyone with Spellfire. Mystara's Chosen.
What's-her-name from Dark Sun who was the only Sun Mage in existence.
The dragon marked from Eberron (particularly those with Aberrant dragon marks).
There was some Ravenloft novel I read as a kid where the protagonist had a unique ability to capture the souls of evil beings (to prevent them from returning). I don't remember the title but I feel like it had Shadow in the name?
What's-her-name from Dragonlance who suddenly acquires the abilities of a potent cleric during a time when clerics don't exist. You can argue that it's the staff's power, but plenty of superheroes derive their powers from an item so I would say it counts.
There was a Mystara series where the protagonist is an ordinary kid who is thrust into adventure and discovers that a dragon god was his father (and that he has dragon godly powers).
There are tons of characters from the D&D multiverse, who wouldn't be out of place if they showed up in a Marvel or DC comic.