This is all conversation since pool doesn't really have any standard set of rules. The rules are whatever the tournament promoter or two players gambling decide to play by. But what I pointed out is a fact.I get you're just making conversation, but the notion that the winner of the lag is gaining to much of an advantage by getting the first and possibly the last break is just a bit too much. We're assuming it goes hill/hill. Why not lag before every game...? ...or maybe best two of three coins flips..? ...oh how about spot shots before each rack...? You have to draw a line somewhere.
As far as lag vs coin. It doesn't make a difference what the choose. Generally I find the person requesting the coin knows they will be out classed in a lag. I don't pity those who make poor choices.