One thing I’m trying to get away from is “sending lesser die hits to weaker PCs if I need to” these days, though. I want to remove that sort of judgment call and just let things happen as they may.

As far as the probabilities on rolling three attacks in one, the others have already weighed-in. It does dramatically reduce the ‘chance’ that any damage is done, but if that time-saver step is worth it for you and your group, cool.

Trivia-
:: As for 10 (or my preferred 6-second Round), an adult human can cross 21 feet in under 6-seconds and become a deadly threat, so multiple swings more or less right in someone’s face (especially by an ambidextrous creature like a cougar) is no stretch of the imagination.
:: Moreover, cougars would almost never attack up-front, instead ‘sneak attacking’ and then running off if they were presented with any serious resistance, and then follow the prey until they could ambush again.

Also, when the claw/claw/bite hits I can send the lesser die hits to the weaker PCs if I need to

(though personally you’d be amazed at how fast the well-trained hand at feet move when fencing…multiple feints, parries, ducks, and thrusts are all possible within 3-5 seconds, let alone 10!)

First and foremost, over the long haul, I’d expect combining damage into one roll to be deadlier to PCs. When damage is split amongst multiple rolls, odds are the PC will take LESS damage. For example: if the mountain lion has a 40% chance to hit (13+ on a 1D20) your one roll method gives a character a 40% chance to take full damage. With the claw/claw/bite the chance of taking full damage is 40% x 40% x 40% = 6.5%. Sure there’s less chance of taking NO damage, but at least you’re not going “all in” every hand!

Second thought: I think that for a claw/claw/bite attack, a creature is probably making multiple swipes and tears…with EACH natural weapon! A player only has one sword to hack away with…an owl bear has two deadly claws and one pecking beak. Now I realize that isn’t consistent with the way I handle two weapon fighting for PCs in B/X… : )

Third thought: Do all animals (like mountain lions) claw/claw/bite? I don’t think so. I’d think they do one “pounce” or maybe one “swipe” (or “swipe combo”). I’m just guessing here…I’ve never been attacked by a mountain lion. However, you COULD re-write every monster entry to make sense to YOUR particular game world. But that might be a pretty hefty project.

I’m no statistician (scared o’ that!), but: While it looks like your conversion of 1d3/1d3/1d6 to 2d6 is fairly close in regards to averaging damage rolls, converting three to-hit rolls to one really skews the odds. As an example, the odds of a all three c/c/b attacks hitting on a 15 or higher is somewhere around 3%, whereas a single attack against that target number is at ~30% odds. (FYI: I have a die rolling app I use to run these sorts of numbers – I didn’t do the math myself.) Thus, if the numbers are right, by reducing all three attacks to a single to-hit roll, you’re opening your players’ characters up to suffering higher average damage amounts each round.

FWIW, ICBWOT (“I could be wrong on this” )