As for holding on a 1 handed wrap, it comes back to one of the basics of defense: MOVE YOUR FEET. You can throw one handed wraps all day without ever fouling if you are able to throw them and continue to move with the ball carrier. In fact, your odds of landing a wrap increase if you can actually be slightly ahead of the ball carrier. One of the best times to throw it is as an offensive player comes off a pick that the defenders just switched on, as you are ahead of the ball carrier.

Physically, you cannot get as much reach throwing what you call a two handed wrap than the one handed variety. When you throw a wrap, you break your top wrist. That’s where the power of the check comes from, and that is what allows you to reach a well-protected stick. It’s a great check for taller defensemen in particular because they have a greater reach and is a much safer check than an OTH check or anything even wilder. If you aspire to be a good defenseman, it’s one you absolutely need to have in your repertoire. The best poles can throw wraps, kayaks, ding dongs and OTH checks in addition to your more traditional fare. 

And if you define a wrap check as a check that reaches the offensive player’s opposite/stick side shoulder/glove college defensemen throw them all the time.

No college defenseman is throwing a two-handed wrap.

This is a great drill if you want to be a surgeon, which is increasingly more difficult to do with today’s technology.  I always teach my kids to be butchers first.  All the control points are still valid, but you are aiming, always for the part of the stick closest to the bottom hand.