That 20 cap is for a relatively ordinary human. Technically even a non-magical Barbarian can achieve a 24 (at level 20), so that's arguably the real strength limit for a non-super-human. But Spiderman has explicitly super-human strength, which means his strength could be as high as 30.
If he has a unique feature that allows him to exceed normal encumbrance limits for purposes of lifting, even your 20k+ criteria is achievable.
Having to allow for anything because of a "unique feature" is certainly one way to take care of a lot of edge cases. <Almost avoid snarkily wanting my cleric to be the Spectre when it's helpful or good for story.>
But seriously, I agree. The actual character of the characters gets too little influence. It's the time when things aren't going Spideys way - when his powers aren't enough, or aren't working, or are countered - that he fights through and shows why he is truly great! (The Thing used to be that way too I think - one anchored Marvel Team-Up and the other anchored Marvel Two-in-One).You're welcome to your opinion, but I think there's a lot more that makes Spiderman Spiderman than what he can bench press.
Does an anti-magic field sometimes give a mage the chance to show their character beyond being a collection of spells? Should a well designed mage class give them enough other skills that they still can (akin to the problem with a fighter needing more when out of combat)?