I think my argument there would be that despite common assumptions, rating is actually a very poor proxy for skill, and an even worse proxy for a good match-up. Similarly skilled players won't always like to play with each other. Nor do I think that win-percentages are the only metric we have to work with -- most multiplayer games have reams of much better data to sort through, particularly in games with high variability of play-styles, player types, and team compositions and setups (games like League/Hearthstone/Overwatch, etc...)

That being said, I would be more amiable to a system that used player skill as a matchmaking tool if it didn't report those numbers to players.

However, I'm not sure I would say that sorting and reporting is usually a side effect or minor mistake on top of those systems, given that many of these games have seasons, rewards, an entire meta-game built on top of their rankings. The rankings aren't just serving the purpose of getting players matched together -- they're serving as player motivators. The responses that players have can't be seen as a purely accidental side-effect when designers are going out of their way to present this information to the player and to encourage the player to pay attention to it.

Hearthstone is a good example here. Hearthstone has brilliant design, but its ladder system is horrible and dumb. It explicitly encourages net-decking and grinding instead of experimentation. Fast decks are objectively better than slow ones with the same win percentage, because ranking is largely determined by win percentage combined with the number of games you can fit into a season.

Season rewards are then tied to rank, so the best way to get new cards if you want to experiment is to build a boring deck and grind. This is despite the fact that for most players, knowing within the first few turns whether or not they're going to win is not fun.

So of course people bot Hearthstone, because before you can build creative fun decks and play against interesting people with interesting strategies, you have to pay the "fun tax" of grinding on the ladder. Everything brilliant about Hearthstone is bogged down by being tied to this kind of toxic experience.

There's no way to say this about such a popular game without sounding naive, and I'll take the criticism, but I do not believe for one second it would be difficult to build a better public ranking system for Hearthstone, especially given the ludicrous amount of player data they have. Even something as simple as balancing rank with deck variety so players got fewer rewards the more times they played the same cards would go a huge way towards getting rid of net-decking.

These systems do increase engagement among very invested players, so maybe that's the only intention. But to heck with engagement -- is laddering at the higher ranks of Hearthstone fun? People do it, people say they enjoy it. Again, I'll take the criticism a statement like this warrants, but I don't believe them. I don't believe the experience of grinding a single 55% win-rate deck for hours and hours is an experience that is worth having or producing.

And when I think about why players do that, the only cause that comes to my mind is, "the game tells them to."