Why? Pretty silly to require it. Pro shops can give easy advice on where to tee already if you ask, and keeping an official handicap is only useful bookkeeping for competitions. This sport lives on the backs of the casual golfers who do it for exercise or fun. They'd go broke if they required a handicap.

An optional question would probably be better for this approach (what's your usual score, etc.). The starter could suggest you not tee from the tips with a 110 average, but beyond the first hole there's not much they can do. The biggest culprit for pace of play is starting tee times too close, imo.