I vote No.  AWPs are restricted on "most pub servers" because most pub servers have noob admin.  The AWP is earned, either by time or winning rounds.  In fact, I propose multiple AWPs per team, rather than just one.  I've been in pubs where they scaled the amount of AWPs per population, so that 1 in every 5-6 players could have an AWP.  Also, AWP was only enabled when there were 10 or more people in the server, so an AWPer didn't kill the server when they went below 10 players.

Your best bet at balancing the teams is to give the losing team money.  The biggest reason why a winning team continues to win is because everyone on the winning team has money while the losing team does not coordinate "saving" and maybe only half of the team will have guns per round.

As to Rival's suggestions, the best AWPer should always have the AWP.  Anyone to suggest otherwise does not understand the point of competition.  To win a round, you do everything necessary.  You logically give the best AWPer the AWP, and the best rifler the rifle.  It's the same logic as planting the bomb.  You plant the bomb at the bomb site in order to increase your chances of winning the round.