Another thing about the min-reraise is many people will push AK or JJ here, putting you on a range that they conveniently beat/flip with. The only way I like this move is if you're trying to instigate a preflop allin, because that's what's going to happen a lot of the time. You also lose out on the chance to flop a set or a straight and stack better hands. So, if you make this raise for information, sometimes you will fold the best hand and sometimes you will give up the chance to stack a better hand. Moreover, if someone does have AA, they might very well call your minreraise and trap you on undercard flops.

I think calling the reraise, or folding with a very specific read, is far better than minreraising unless you are trying to instigate an overaggressive opponent into pushing a worse hand preflop. The minreraise here is FPS in my opinion.