sstorkel

Not only do you have to worry about the angles of the tubes, but you also have to keep everything in the same plane. Try this: cut your seat tube to length, miter it, then slip the lugs on either end. Now grab both lugs and twist them in opposite directions. What happens? They'll move. If you've mitered the tube poorly, they may move quite a bit. What does this mean? When you insert the top tube and the down tube into the twisted lugs, you won't have all three tubes in the same plane. A jig, even if it's a cheap plywood one, will help keep everything in the same plane so that you don't end up with the head tube or rear triangle cocked at some odd angle.

You have some freedom to change the tube lengths. You couldn't, for example, make a 5-foot long top tube. Not that you'd want to, but you get the picture: fitting a tube that long into a bike that used normal-length tubes everywhere else would require really wacky angles... which your lugs won't allow.

Only if you want the bike to hold together over time. Ideally, you want the lug to reinforce the joint. You don't want the lug to be the joint. If you just make straight cuts on the ends of your tubes, then all of the stress will be concentrated on the lug at some point. If your tubes are well-mitered, your brazing will lead to a direct connection from one tube to the other and the lug will act as a reinforcement of that joint; much stronger that way.

Besides, only a talentless hack would stick unmitered or poorly mitered tubes into a lug and call it a bike...