Exactly this.

I get why the OP is disappointed. It would be awesome if there was some sort of online way to compare skill outside of the tournament format with some assurance that it's reasonably legit. For example, I play FPS games on the PC but I don't have an interest in tournament play. Still, I can see how I rank globally in casual play (though, it should be noted there is plenty of abuse even in live, casual play to boost rankings).

Unfortunately there's too much variability game to game. Tournaments and leagues are the closest we have to measuring skill with the fewest number of random variables.

It would be kind of cool if games were shipped with a "high score settings mode", which is the standard settings for achieving high scores, outlane peg hole position, etc. Then if players recorded their games they could show that they opened the coin-door and put the game in that mode prior to starting the game, as well as other physical settings. Or it could be agreed that factory default settings are used for that purpose.

Still, without an extremely consistent tilt mechanism, which I think would need to be digital, that one difference can have a major impact on score.