Either a tremolo?
Yes the one with medium frets and fender type headstock has a tremolo bridge but i dont use it because it goes out of tune.
the springs counter the tension of the strings.
if the springs are stronger then the strings, you wouldn't be able to 'whammy', so the springs are equally strong or less. So you're not fighting the strings anymore, you're fighting the spring and because of how forces work (cantelevers and such) it's easier to let the bridge pivot while bending the strings then to 'not' do it (simple physics).
Than what is the right answer? could it be the fender type headstock?