The way you strawmanned per-minute stats by using an extremely small sample size was what tipped me off to your inability to be convinced. I'm not sure it has anything to do with your career.
By the way, there are no stats that are robust to extremely small sample sizes.
For the non-statisticians in the room who might be interested, per-minute stats (or, better, per-possession stats) are typically used to allow better comparisons between players who receive different amounts of playing time than per-game stats. There are obvious reasons for this. There are, of course, caveats to per-minute stats just as there are to any other measures. Outside of small-sample size issues, per-minute stats should probably not be used to compare players who have extreme differences in minutes per game, because a player who plays fewer minutes may not have the stamina to keep up his per-minute numbers with a lot more court time. Additionally, some players may have different roles - a guy who plays exclusively off the bench will likely be faced with better defense (and better offensive companions leading to lower usage) if he moves to the starting lineup - so comparing players with different roles can also lead one to making some bad inferences (though this caveat is not restricted to per-minute stats). But so long as one understands the context, per-minute stats are a perfectly reasonable and altogether not foolish way of looking at production.