The solution is pretty simple to me.
If a player goes down requiring a game stoppage, that player must be removed from the game for medical evaluation in the locker room, until they are cleared to return by medical staff AND at least 1 minute of game clock has elapsed or there is a change of posession, whichever is longer.
Also, when the game is stopped due to injury there can be no substitutions on the injured players team, except to sub a player for the injured player. If the same player goes down requiring a stoppage more than twice a game, they are required to go to the locker room for the remainder of the game for appropriate medical treatment.
NCAA makes a rule like that for "player safety" and flops stop completely.