So I went out for lunch just now, and while I was out, I had a train of thought.
Suppose we remove the first seven levels of Fun, and imagine a new player going through the game. What specifically would they learn from each level?
8 - After trying out climber and floater and finding they're not useful here, the player tries the blocker and discovers what it does.
9 - Similarly, player can be expected to pick up the basher.
10 - Floaters. The obvious solution also uses a blocker, but that's already been taught so that's fine.
11 - One-way wall and climbers. This solution is much more complex, using all the skills introduced so far, but the new information needed is limited enough that the player can discover the solution.
12 - Dealing with RR 99, builders to get out of a pit (a safe environment where mis-clicking won't lose the level).
13 - Diggers. Okay, this is not how I would choose to introduce diggers, but the level does show you what they do, as well as emphasising that a small change in height can make a fatal fall safe.
14 - A longer, safe environment to put together what you've learned so far.
15 - Building over the gap is slow, so you need to control the crowd. (More so in the Amiga/Mac version with its higher save requirement.) There are several possible ways to contain the crowd, so the player can find one that suits them best.
16 - Not much new here, but it can look imposing at first if you don't realise that several builders can make a long diagonal bridge.
17 - Traps. Again, a funny way to introduce them, but the save requirement is low enough that once the traps hit, you can block up top and still pass the level. Also introduces lemming arithmetic in that you only have to save 20 lemmings and have 20 floaters.
18 - Bombers. These get shown in isolation, since if other skills are available there's little reason to use a bomber. Although the player has probably worked out the "two blockers, bomb to release" method by now.
19 - Walking long distances. Okay, this one is meaningless filler.
20 - Quick actions required at the start.
21 - A better introduction to traps, showing that you can build over them and be safe. (In Lemmings Redux, we specifically included this level to provide an early introduction to traps.)
22 - Special graphics are a thing.
23 - Hidden flamethrowers and hidden exits are a thing. Yay?
24 - Dealing with RR 99 where it isn't as simple as blocking on the edge. I remember this being quite a challenging level when I first played the game.
25 - Mesh-like terrain and lemmings' tendency to flow upwards through it.
26 - Another filler level.
27 - Dealing with a fatal fall by going round, or by building a platform underneath. This stands out as an excellent Fun level.
28 - Isolating a worker by sending an athlete out of a holding cell.
29 - Navigating a zigzag bridge through a narrow gap.
30 - Lemmings can squeeze into tiny gaps. Directional select (on ports that include it).
In short, pretty much every level teaches the player something new; 19 and 26 are the only levels that are pure filler. And all this teaching is done by allowing the player to discover the mechanics for themselves, and (most of the time) giving them enough leeway that it doesn't matter if they try something that doesn't work out. The Fun set actually turns out to be a really good introduction to the game, which is funny because that happened more or less by accident -- the hard levels were designed first and then the devs just made 20-of-everything repeats to pad out the easy ranks.
(Of course, it's not perfect. A couple of absences stick out: there's no level that introduces steel, until you hit Tricky 9, which is oddly late. And there is no level at all in the 20-of-everything portion, even including Tricky, that introduces miners or encourages their use. So the player may well not get the practice they need at estimating where a miner ends up. Maybe that's why "How do I dig up the way?" was considered suitable for late Taxing?)
Now that I've written this post, I think that making a pack that's suitable for absolute beginners and does the same job of introducing a mechanic or concept with every level would be a very interesting challenge. I might try that at some point :P
Ah yes, of course - Fun 10!
Again, interestingly you use a miner to achieve said 100% solution!