I don't use it because I feel it's a solution to a problem that is actually occurring with the DM's means of determining uncertainty rather than a problem with the game itself. The example it gives is the "ludicrous" result of the rogue knocking down the door the fighter couldn't. What it leaves out is the context surrounding this situation which may help determine whether the result was uncertain at all. If the party, for example, isn't concerned with time or noise or anything else - basically there's no meaningful consequence of failure - then the fighter just succeeds with no reference to mechanics in my view. The fighter might also be able to retry indefinitely in which case the rule on retries kicks in and the fighter has automatic success anyway. As well, since the DM decides whether a check is made (passive or otherwise), if I am bothered about an outcome where the rogue busts down the door the fighter could not, I can just decide the rogue's attempt fails outright.
The DMG also points out a downside: Once an ability score gets to 20, checks of DC 15 and lower become automatic successes. Smart players will then just match the appropriate character to whatever check is needed, which may cause DMs who want to include risk of failure into the equation to boost DCs which defeats the purpose of the variant in the first place.