Why Does Magic Use The "Paris Mulligan" Rule?
A few points:


"Good for the game" is drastically different if you are playing competitively or casually. Competitive Magic should encourage good deck building and make it as fair as possible to each player. Paris mulligan vs. lenient paris mulligan isn't going to drastically change the fairness between the two players at the table and adds more complexity to an otherwise already complex game.
Learning when to mulligan is actually a very useful skill in Magic. Making it easier to stomach doesn't necessarily make it a better mechanic. Designing (and testing) decks with 7, 6, 5 card hands is very important. Likewise when playing against particular decks. Some decks struggle against a 1 card advantage. Some decks shrug it off and keep pounding.
Real life Magic mulligan problems can often be solved by shuffling properly. People can get lazy in their shuffles and tournament nerves can make it worse. Take the time to adequately shuffle your deck each time you draw a hand. This is especially true after a mulligan: Simply cut-shuffling a few times will result in you drawing the exact same cards you just threw back.
When playing casually, I recommend players just draw back up to 7 after a mulligan. I would rather play against a deck's best chance than roll over someone with a 5 card start. Casual games should be fun more than fair; if the lenient paris mulligan is more fun for your play group then that is how you should play.