The amps are far more capable of such limitations.
I agree. Tweed amps are extremely capable of having limitations.
The Chicken picken (picking) or distorted blues garbage used to demo tweed clones is probably akin to high gain amps and super distortion pickups being demoed by some head banger going wee, wee, wee all the way home. You wouldn't drive an Escalade and ask why you can't get more than 14MPG, would you?