Take this idea to its logical conclusion.
If a player is never allowed to make a move that puts them in a situation where they will definitively lose; then when the opponent is one move away from a putting the player in checkmate, the player would not be able to perform any move other than a move which prevents said checkmate.
In other words, the opponent isn't actually able to act on the checkmate as the player is forced to resolve it before it happens. So what can the opponent do? Well, he can manufacture a situation where the player cannot avoid the checkmate next turn, a so-called guaranteed-mate-in-one.
Wait... We just said that a player is not allowed to make a move that causes them to 100% lose this game. This guaranteed-mate-in-one is such a scenario. Therefore, the player's previous move would not have been allowed.
In other words, the opponent isn't actually able to act on the guaranteed-mate-in-one, as the player is forced to resolve it before it happens. So what can the opponent do? Well, he can manufacture a situation where the player cannot avoid the guaranteed-mate-in-one next turn, a so-called guaranteed-mate-in-two.
Wait... We just said that a player is not allowed to make a move that causes them to 100% lose this game. This guaranteed-mate-in-two is such a scenario. Therefore, the player's previous move would not have been allowed.
In other words, the opponent isn't actually able to act on the guaranteed-mate-in-two, as the player is forced to resolve it before it happens. So what can the opponent do? Well, he can manufacture a situation where the player cannot avoid the guaranteed-mate-in-two next turn, a so-called guaranteed-mate-in-three.
...
I hope the flaw is apparent here.
The only way to resolve such a game would be through players resigning because they tire of the game, not because they've lost.