Blind stealing / Valuing cards from Button

Alright, I thought about this a while. Is it better to call a 3-bet from the button with every card you raise with when only against blinds.

e.g.
Hero open-raises, SB folds, BB raises, Hero calls.

If we do this our hand range is very large, which means that we can have AA or we could have K-5s. If we cap with JJ-->AA then our hands we steal with lose value and our hands we cap with are better defined.

Is the value lost by not capping gained by the fact our hand range is now a lot more vague, e.g. we get paid off better because they can't put us on a hand.

True