What this rule would do is effectively add those few more minutes to the regular play. Why not make the match 23 minutes long then? It would be the same. Hence I see no logic behind your suggestion. How do we resolve tied games if you want to remove the first kill advantage from the competition?
Long and very passive games are boring for the viewer. The teams must resolve the match in 20 minutes as the tournament must keep going. First kill advantage puts pressure on the losing team to act up. One of the biggest dick moves of competitive play is to escape from the engagement and abuse the timer rules. It would be unfair to the team, which does not have the upper hand could escape their destiny instead of confronting with the opponent. That would hurt the players wanting to fight, but unable to keep up with fleeing enemy.
I know that I'm always theorizing too much, but I believe that The rules must be free from any possibility of their abuse.
I'm going to assume two situations and show you on the example:
In case 1 (current rules) Team A got the first kill advantage. Team B now must attack and dominate Team A or they will lose the game. If Team B can prove that they're better, the win will be theirs, otherwise, if they are worse than team A, the team A will win.
In situation 2 (Spud Nick's proposition) The game is tied. Team A knows where they have made their mistake and wanted to confront Team B again. Team B is weaker, so they choose to be dicks and escape. The regular time ends and we get into overtime (Team A got the first frag, but it doesn't matter anymore). After that, the game is being resolved with coinflip just like in every case of the tie and Team B wins. Team B in this situation instead of inevitable defeat has the chance of 50/50 to win the match still by abusing the rules.
To be very honest there is no perfect solution to the escaping as the winning team (in case the game is not tied) could still escape, but in such situation the team which is better and was able to score in the initial engagement still wins. This sentence is correct because it is possible to win an engagement without even losing any permahull; hence the better team is the winner.
Current rules: Winner is always the better team
Spud's proposition: If you're weaker than the opponent just be dick, and you still have 50/50 chance to win.
That's why first kill advantage can't be removed.