Number of games on Steam and number of games with achievements / cards (just some statistics)

Totaly agree with your reasoning but you have to understand that all of that is subjective and that making a comprehensive list based on those points would be virtually impossible.

Achievements nowadays show you things you have done for yourself in the past. I remember myself that I played a lot of games to maximum level, finish everything and collecting everything (just because I want to have everything) so I can say "I mastered the game completly".
Some achievemnts today are just annyoing or stupid (e.g. The Stanley Parable - Dont play the game for 5 years). I mean come on! Sometimes they change/update achievements (Hero Siege) or they broke (Knights of Pen & Paper +1), so it only luck if the developer update the broken ones. Most games dont have achievements that let you play the games again. They have some just they can advertise with them, but they are totaly senseless.

It's hard to say what achievements are good and bad, as they target different people.
The "hey, you just did what any normal person would do anyway" kind of achievements (beat a level, kill an enemy, pick up a weapon) are there for newer people. It's basically positive reinforcement, and it helps people who are not very good at games or who are relatively new to them feel like they are doing well. It also helps reinforce the intended playstyle ("hey, I just got an achievement for doing a melee kill, and that also gave me a bunch of ammo, so I'm doing the right thing!").

Then there's the "kill X of Y" or "Collect 1000 feathers" kind of achievements. They are there for completionist, to give them something clear to strive for.

Then there's the alternative challenge achievements. They are there to highlight challenges that the developers thought seemed fun, but could not be easily implemented into the game itself without it feeling "gamey" or requiring a lot of extra work. This is the last category you mentioned.

So none of these are really right or wrong, you're just not the target audience for most of them.

There's one final achievement type... the "hey, I'm in your achievement feed now so everyone can see that you play the game. Free advertisement!" type.

The kind of achievements are quite different for every game, hard to measure, but that wasn't what I was looking for.

I could tell you the reason why I was interested in checking the stats from the start:

If you look at my recently played games on Steam you can see achievement stats (right hand side) for all played games with achievements, stretching back the last 20 or so days (games played before that won't show achievements, even if there are gained achievements for that game). When visiting some profiles, I don't see a single achievement among the recently played games, so I was just curious to see if games with achievements are not that common, which would make it plausible to play 20+ randomly selected games in a row during 20 days, that you can't get achievements in.

Turns out it wasn't, and the reason why achievements are missing on some profiles might simply be that those users don't play that many games for real, and mainly use their accounts with card farming software.

As you said, many (most?) games with achievements have the kind that will drop without any real effort, so for most games, if you have played them for real for a couple of hours, you're very likely to have gained at least one achievement.

I imagine achievements are harder to implement as you have to modify the game, while you don't need to even touch it to have it drop cards. Also cards bring you more moneys, so there's a motivation as a bonus.