1) Because the wind may shift.
2) A stern anchor won't keep the boat from yawing, it will just stop the boat (with a jerk) when it reaches the end of the line.

What you really want, is something that keeps the boat pointed into the wind, so that it doesn't want to sail away in the first place - which is just what an anchor riding sail does.

I've helped run several regattas using a friend's Beneteau 44 as a signal boat. It's keel generates enough lift that, when at anchor, it will sail off to one side, stall, drift back, catch, and sail off to the other side all day long (which is not what you want happening to one end of the starting line). A small sail hoist up the backstay keeps the boat pointed into the wind and it stays put very nicely.

Regards,
Eric