We discussed this further in #neolemmix today. I watched rtw's playthrough of the level Icho mentioned, "Nick of Time". I can see the elegance in the way the crowd is not contained, but instead two worker lemmings are used to construct the route before they return from a journey along a walkway. (This is coincidentally similar to my level "The Hotel in Hell".) However, the time limit doesn't contribute directly to the elegance. It serves to prevent a backroute where the crowd is contained while a single worker lemming builds to the exit, turns on the steel platform the exit stands on, and goes back to build a landing platform for the crowd. This backroute could easily be prevented by alternate means.
Icho mentioned that there are other levels where the time limit is needed that, in his opinion, would not be so easy to fix by other means.
I have been thinking about this, and I think that levels with time limits can be grouped into the following categories:
#1 "Just a Minute" type: The level would be trivial, and the entire puzzle is to solve it within a time limit.
#2 Specific-solution puzzles, where the time limit is used to prevent one or more backroutes. (There may be multiple intended solutions, like the left and right exits in "Buridan's Lix", the left and right sides in "Close to the Edge", etc. However, these are more like multiple puzzles on the same level, rather than making the level into a Type 3.)
#3 Resource management levels: There is no specific intended solution, but the lemmings / lix must navigate through a complex terrain within the constraints of a limited set of skills. This does not mean "anything goes", as the level is spoiled if there is a solution (such as a floor or ceiling route) that is much simpler than the designer intended.
In levels of this type, the designer may impose a time limit as an additional constraint -- I mentioned the example of "Deserted Cities of the Heart" from one of namida's recent videos. In this case, running up against the time limit usually doesn't mean "redo and release the crowd earlier", but rather, finding a different way to approach the obstacles that permits solving in time.
#4 Multiple hatch levels where the purpose of the time limit is to enforce multitasking. Back in original Lemmings, this added challenge, which means a certain amount of frustration, and also a certain amount of satisfaction in overcoming the challenge. There's no point now in debating whether this type of level was a good idea: it is completely redundant now that there is framestepping and rewind.
#5 Levels where the time limit is primarily aesthetic.
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As I mentioned to Icho: The evidence from looking at the Lix community set is that types 1 and 2 are extremely rare (one example of each), so the debate should centre around whether the good of allowing time limits in type 3 outweighs the bad. Icho has more experience of NL and Lemmini levelsets, and believes that type 2 is more common than I am allowing. Namida has made some excellent type 1s in NL, so there is the consideration of keeping open the possibility of future designers making more type 1s.
Back when we first debated time limits, NL was relatively primitive. It has now developed into a fully viable outlet for level designers. I would be quite happy to see time limits removed from Lix, and then I would still be able to use NL any time I got a level idea that absolutely depended on a time limit.