If coaches started treating the 4 minute mark as 0:00 on the clock then they would start fouling earlier. Your down 12 with 7 minutes to go the coach might start fouling to get it down to 3 or whatever for the first under 4 stoppage. Coaching would change and adjust. The fouls would just happen earlier. All it would take would be a season or 2 of data to show if that would bea viable strategy for this type of set up
Fouling even a bad FT shooter (65%) is on average 1.3 ppp. That's better than Villanova 2018 or Wisconsin 2015 offense.
And that's the worst case scenario for the offense (coaches can pull bad FT shooters with between 6 and 4 minutes left if teams actually tried it). Teams who shoot FTs every possession are the greatest offense of all time.
The only benefit is somewhat increased volatility (especially with 1 and 1, which I'd consider removing like NBA if switching to Elam), but it's a losing proposition over the long term. It also harms your offense as it is almost impossible to get transition opportunities after FTs.
Again, the only reason coaches currently do it is to lengthen the game (other than the hack-a-x). There is no reason to lengthen the game with the Elam ending.