I'd rather tend to making Nessie a trap consistenly then. However, it still differs from a normal trap, because the head is terrain you can walk on while other traps are just objects that can be walked through.
There is however some inconsistency in the tilesets themselves.
Take for example the Menacing set: There are snakes that are terrain and there are snakes that are traps (the ones looking sideways). A first time player will still need some time to figure this out, especially since you can't walk at all on the heads of the trap snakes, while the others are stable terrain.
The features like replay, rewinding and true physics mode are blessing and curse at the same time, I'd say. For me, they are mainly "anti frustration tools", saving you from annoyances. Purists of the original game would probably consider them cheats; you could make a case that in the original Lemmings, the frustration of missing an activation at a crucial point was part of the experience of the game.
Also, what the point of a level is is kinda subjective, isn't it? Take the cross promotion levels from Lemmings (Beasts, Menacing, and Awesome). None of them is particularly difficult, but they look cool, they have an unexpected change of music, they just mix things up.
I understand your point of view of NeoLemmix being all about puzzles, since I used to play Star Wars: Pit Droids back in the day (or now again on the iPad). There the levels are even called "puzzles" and you have to place all skills beforehand (=like "before Lemmings even come out of the trap door"). It's all about "solve in your head first, then execute". However, the type of challenge these puzzles pose is always very similar. There are no "quick reaction" challenges in Pit Droids, there is barely "learning by doing" or "trial and error".
In NeoLemmix, also levels like We all fall down are pointless, because it's totally obvious what you have to do and you can play the entire level with the pause button switched on, rewind every time a single lemming splats etc. But just because you can, should you? It's clear this wasn't the point of the original level. It's the old "with great power comes great responsibility" thing
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The NeoLemmix features imho are both an argument for and against "annoyances". You could say it makes them pointless, or you could say it makes them unproblematic, because whenever one is fed up searching for the exit, they can use the true physics tool, while those who like this type of level can keep on trying the "original" way, a.k.a. the hard way
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I used to create levels in WinLems, which doesn't have these features and only has manual steel rendering. This invited me to create levels wih bashable steel - or with normal terrain that can't be bashed through. So I created this level called "Hallowed Ground"; it even says in the title that there might be a reason this doesn't work as usual
. Yes, my brother had to rethink for a second, but he made it through without major frustration.
PS: "X marks the spot" also has a hidden trap, that fire trap, that is even hidden behind a supposed exit on the left side. The level gives you a hint for the exit on the right, but at the same time fools you to believe there were exits behind the Xs on the left, too - instead, one has nothing behind it, and the other one, even worse, has a trap instead. Oops, the first time you try, you're screwed - but then you'll remember.