I had multiple surgeries as a child, and i wouldn't hesitate to let my children go under if it was for an actual medical procedure.
Breast implants, or a tummy tuck, not so much (i suppose, at 17/18 i'd consider a breast reduction if they had gigantum boobs though).
But most drs i've talked to rarely suggest surgery unless its genuinely necessary - and i'd still freak out, and double guess myself, but i'd be ok with saying yes. - with some imput from my kid/s, but that would depend on their age of course as well.
[necessary! - that certainly means no genital surgery, unless genuinely warranted ]