The doctor? you mean the mohel?
Tremendous risk? How big risk? Are there studies? 1 in 1000? 1 in 10000? 1 in 50?
Bris has very little risk? Are there studies?
What is the risk in building a sukka? More or less than metzitza? People fall from ladders, cut themselves on saws, hit themselves with hammers, puncture with nail guns…
What is the risk of chanuka candles? Shabbos candles?
Shechita? People get trampled by cows…
Mikva? people drown (I know a case)
Fasting on yom kippur? people die, the doctors are sometimes wrong..
Drinking on purim? (ok, forget that one)
Breaking a glass under the chuppa? people have cut their foot.
Dancing on simchas torah? People have had heart attacks, have broken legs, etc
Throwing candy at aufruf and bar mitzva? Hitting in eye, kids getting trampled…
Staying up on shevuos
trying to get home in time for shabbos
etc.