It is broken or they wouldn't be thinking about it. If you reject the premises that 1. there is something inherently wrong with a tie and 2. current and proposed overtime remotely resemble football, the solution is easy: drop overtime altogether and accept that sometimes there is no clear winner.
The 2-point shootout idea is absurd. If you insist on overtime, play an extra 6 or 8 minute quarter. The score at the end of the 5th quarter stands, even if in a tie.
Please read the OP, which I have quoted here. Hopefully, you will see that I don't advocated for alternate possessions from the opponent's 25 yard line.So starting alternate possessions from the opponent's 25 yard line isnt a subset of the game?
Sounds like you need to rethink your argument