As well as this community, I've been part of other puzzle game communities (primarily Repton and DROD) for many years. The same discussion comes up in all of them. That said, what follows is just my opinion -- I don't pretend that having had this discussion before has given me any kind of "definitive" answer.
Or, can alternatives be happily accepted, but only if they're better than what's intended? Or even, should alternatives always be happily accepted because the player has found a different way to beat your level with the skills and situation that you've provided?
I don't think there can be an "always", because what's best depends on the level and depends on what the designer wants for that level. Allowing alternative solutions makes a level easier -- sometimes drastically easier. Of course, it's good for the community as a whole if a range of difficulties are represented. It's usually good for packs to cover a range of difficulties as well, although I have a lot of respect for packs that start hard and stay hard (or get harder) if the designer can pull it off.
So, sometimes "alternative solutions are okay and I'll just sort this level into an easier rank" is the right choice -- obviously for an aesthetic value of "right", since designing level packs is not a moral decision. Sometimes the level works best as completely open-ended or 20-of-all. Sometimes you can split it into easier and harder repeats. And sometimes, you have the level that you really want to keep as one of your harder levels and it's worth defending the intended solution and cutting out backroutes. It depends on a lot of factors: how elegant the intended solution is, how much easier the alternative is, whether the alternative is elegant as well, whether the alternative is enabled by a simple oversight or complex logic... and at the end of the day, simply the designer's personal preference.
I'll give a few examples.
"Let's go camping" (Genesis Sunsoft 19 / Redux Lunatic 27) is completely spoiled by the backroute of turning round all three lemmings on the top level with just a digger and builder. This solution isn't interesting at all; it just repeats actions you've had to do many times before as components of other levels, and it's very easy to spot, so there's little time spent engaging with the puzzle and little satisfaction from beating it. The Redux version, which prevents this backroute, is a
much better (more interesting, more enjoyable) level. Even so, it doesn't enforce one specific solution; it just enforces the general route of using the full level area, leaving the specifics up to the player.
"Postcard from Lemmingland" (Tricky 19 / Redux Zany 19) is a case where the unintended solution is quite a bit harder, both to find and to execute. This makes it perfect for a talisman -- both solutions are still possible, but if you find the intended solution first, you can keep looking for the harder solution.
"Five Alive" (Wicked 16) is, in NeoLemmix, completely spoiled by the backroute of using the bomber exactly at the terrain-steel boundary to turn the lemmings around. This is why it didn't make it into Redux; we couldn't find any good way of fixing the level, and the level with the backroute wasn't interesting enough to be worth keeping, even in a lower rank.
"You only get one bash at it" (Lix Hopeless 38) is a level built around a particular idea: not just a theme, but one specific thing that I wanted the player to do, and the level hides the fact that this action will solve it and has red herrings encouraging the player to look elsewhere. If you don't have this one idea, you haven't solved the level. So I felt I had to cut out unintended solutions, even to the point of requiring 49/50 saved rather than the original 48/50.
"The Hotel in Hell" (Lix Hopeless 6) is a case where, each time Simon found an unintended solution, I decided it was worth preventing it. There isn't really a single core trick or linchpin to the intended solution, but it has a coherence as a whole. You have to work out which lemmings to send where in order to construct parts of the route, and the right order to do things in to make everything possible and not lose more than you're allowed. I felt it was a better level for making sure that only the intended solution is possible, but that's a judgement call and someone else (if they had built the level) might have decided differently.
(I could go on with other examples of levels where I've accepted backroutes and levels where I've prevented them, but you get the idea.)
A scenario which comes up many times is that a designer will create a level, and a player will find a way to solve it with a solution which isn't intended. In that scenario, the player has "beat" the designer.
But now, the player cannot solve the level. They don't know the obscure trick or they can't quite piece together the extensively complex series of actions which must be done in just the right order. Finally, the designer has "beat" the player.
But, neither of these situations is really what anybody wants.
Firstly, there's no such thing as a level a player can't solve because they don't know the obscure trick. If it's possible for the creator to come up with the trick, then it's possible for the player to discover.
More generally, it's not really possible for a level to "beat" the player in this sense. If the player can't solve it, they can always come back another time and try again. However, most players will have some levels they never solve, because we have limited time and solving levels is only a hobby. And that's okay!
So, rather than thinking in terms of either the player or the designer "beating" each other, I suggest thinking of the designer as a provider of entertainment. If the player gets enjoyment out of solving the level -- whether by the intended solution or by a backroute -- that's great; but fixing backroutes may improve the product and make it more enjoyable for the next player to come along.
