I kind of agree with the article in some places, but I disagree that achievements and trophies are necessarily the Bedazzler rhinestones of game design, sprinkled inartfully atop a pre-existing game design. I do feel there are a lot of achievements that fall into the author's concept of variants (which oddly the author dismisses as the worst type of achievement, and then uses as the basis for his suggestion of an alternative system), and the issues the author brings up with having those gameplay goals remaining achievements is essentially "well, the player didn't set out to do them at the start of the session, so they are necessarily bad."
What? Why? Why are achievements you get accidentally for "emergent" actions a bad thing? Because a developer thought this was a thing that could happen in the game and made an achievement for it, they've ruined the discoverability of that action? That makes sense if you're the type to reach all the achievement descriptions beforehand and set out to earn them all. But news flash: you didn't invent the concept of blowing up three dudes with a grenade, person who is playing a game and got that achievement. Even if that achievement didn't exist, chances are someone on the development team thought that would be a cool thing to do, and perhaps even planned for it and encouraged that action in the game design.
And the idea that achievements are just arbitrary goals plopped on top of a finished game feels wrong to me too. To be fair, I think some game designers really don't care about achievements and do see them as a necessary evil rather than another game system to incorporate; my favourite game of last year, The Witness, is a good example. But not everyone thinks this way, and to lay the blame for poorly thought out or straight up boilerplate achievements at the feet of the system itself seems to throw the baby out with the bathwater to me.
I also think making variants that lock you into a specific goal is too confining. Sometimes achievements can overlap, or encourage different playstyles in the same session without being mutually exclusive. Under the author's proposed system, I'd have to quit one game session and start another with a different set of rules. And for what gain in the end? The knowledge that the player didn't do anything outside of the game rules you laid out for them at the start? Not every game is a straitjacket, and sometimes fast and loose play is encouraged. Locked-down variants would seem to discourage that type of play. It's especially interesting to me that the author says that allowing players to pursue multiple goals at once is bad because it just means they'll pursue the easiest one based on current game conditions. One, why is that a bad thing, and two, does that in fact always happen? Lots of people on GAF, for example, talk about adding extra challenge for themselves by imposing constraints that aren't even supported in the game itself, and require a great deal of discipline on the player's behalf (ex. one-life runs in games that don't care about lives).
Finally, I'd say that even the "mandatory" or easy-to-get achievements have some worth. Achievements, after all, are a social system as well; you can show them off to people, your friends can compare themselves to you, etc. On GAF, people have used achievement statistics to determine things like how often do people finish games, or how often do people drop a game at a certain chapter. With friends, it can be fun to compare how far each of you are into a game, or whether one of you did a thing while the other person didn't. That's all stuff that sits outside the game design, true, but I think that stuff has real merit for a lot of people.
I think ultimately this article comes from a perspective that says game developers should impose more authorial control (and more intentional authorial control) over the experiences they give to players. Given that the author is a game developer, that's a perfectly understandable and valid stance to take, and I don't think they're entirely wrong. But I think it might also be a limiting perspective.