Safer riding physically attached to the bike.... you serious??
Absolutely - you have masses more control over the bike so the chance of getting into problems are reduced and when you DO get into problems they always unclip quite safely.
At least that is my experience and I have ridden Morzine (including doing the jumps at the park in Les Gets) and Spain doing some VERY technical switchback descents (with Switchbacks) and I was MUCH happier using my SPDs. (I even took my flats to Morzine just in case but I wasn't as comfortable with them).
Me (with SPDs) at Les Gets

Me (on flats) in Bubion - please note the lack of control I have over the bike

Bubion again, clipped back in...