TL;DR1. Players will almost always try to backroute levels, even if unintentionally.
2. This is not always due to a player's ability, it can (also/instead) be their preferred playing style that dictates their approach.
3. Indicate your level's difficulty as accurately as possible to maximise the chances of the player approaching it in the way you'd prefer, and - ultimately - enjoying it more!
this pixel precision was not at all part of the intended solution, but the level didn't outright prevent you from attempting the pixel-precise approach either.
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Hence, I'm beginning to wonder whether I should purposefully reduce the complexity of levels on a conceptual level to prevent people from inflicting such unintended pixel precision on themselves.
This is an interesting question. It almost goes beyond asking "should we prevent backroutes" to ask "should we make it so that players don't even
consider backroutes?" (Note that this particular interpretation is in the context of the remainder of the OP, which discusses backroutes in relation to entropy | also note that I'm aware that you've differentiated pixel-precise solutions from backroutes, however we can probably agree that they both stem from the same approach.)
The fact is (and I think it's a fact that content creators would do well to accept),
players will nearly always try to backroute a level, even if they don't mean to. It is nearly impossible to guess how every player will approach your level, and the more complex it is, the more likely it is that players will try to backroute it (again, even if unintentionally).
I don't mind a good backroute. It's often a very satisfying way of hacking through a poorly-designed/overly-complex puzzle
and, by the same sword, if someone backroutes my level then more power to them, congratulations.
I do think the path on the right should only look inviting to someone actively trying to backroute the level. So I'm kind of glad to "punish" that attempt by making them feel eventually that this shortcut is futile 
Maybe you're joking
However, to address the point; backroutes often come about from innocently trying out a solution that you genuinely think will work, as opposed to "actively trying" to backroute a level, so this approach doesn't solve the problem if you're attempting to reduce player frustration.
As I see it,
there are 3 main ways to respond to your level being backrouted:
1) Back to the drawing board to fix it; I only ever do this if I particularly like the level concept, and the backroute has come about purely as an oversight.
2) Leave it as-is, and/or move it to a lower rank; this is usually if the level is decent enough, and the backroute is an equally satisfying solution. Or, you simply don't mind that the level can be backrouted!
3) Scrap it; if it's so easy to backroute, it probably isn't a very good level anyway. This particularly applies to ridiculously over-complicated levels. Yuck! Take the backroutes as a sign that the level is too uninviting to be solved properly.
If I want to decrease player frustration by preventing them from getting on tracks that lead to self-inflicted pixel precision, I necessarily also have to reduce the entropy of the level, so that the player doesn't even consider going along a path that might lead to frustration.
Rather than thinking in terms of preventing the player from considering a backroute or a pixel-perfect path (which is what has lead to your consideration of reducing the level's entropy), what's needed is simply to
place the level in a higher rank (as Icho suggested): indeed, if as you say "it's not very obvious which skill has to go where, or which path you can take", then
it's probably a more difficult level than you think it is. Keep the entropy where it is, and indicate the difficulty accordingly. Players are generally far less likely to stick with hackish, backroutey solutions on levels in higher ranks (that is, if they're determined to find the correct solution - more on this in a moment.)
It seems that what you're trying to do here is expect too much of average (or even above-average) players. Most will (often inadvertently) try to backroute a level that appears to be too difficult from the offset: this is natural, even if not intended by the player themselves. If they're anything like me, they'll take the path of least resistance wherever possible. Case in point:
For the Lemmings World Tour levels however, some of this pixel precision came from what I would almost call rookie mistakes. Like overlooking the save requirement, or the fact that you can have a lemming finish a skill and turn him around with a walker, rather than wasting the walker on canceling the skill without turning the lemming around
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perseverations in the form of "not being able to let go of what we think must be the correct solution" are one of the greatest pitfalls you can run into in Lemmings in general
Interesting stuff
I see what you mean about these being "rookie mistakes", since it's important to take in as much detail about the level as you can before attempting to solve it. However, casual players such as myself tend not to do this; I prefer to simply get into the level and start trying things immediately. The more custom content I play, the better I'm getting at visualising solutions before I go ahead and try anything, but my preferred method is nearly always "hands-on, attack the level".
Now - I am by no means a rookie: I have solved both of the original games and a decent handful of custom packs, and I'm almost finished with
Lemmings Plus III, which is one of namida's hardest packs. Granted, I've had a bit of help here and there (and, incidentally, since I'm trying to solve rank 4 of
LPIII without help, progress is slow to say the least!), but I'd say I've solved at least 80% of the packs I've played with my own little brain. However, I still have my preferred playing style, which is to
solve the level however I can rather than try to work out what the intended solution is. This is just a matter of preference, and no amount of experience or increase in my own ability is likely to change this. If anything, it'll just make me even better at finding backroutes
The point here, and indeed the flipside of all this, is that
I tend not to mind if a solution I'm trying doesn't work out. Chances are, I didn't spend too long on it in the first place and I'm all too happy to quickly get onto trying something else. And, if a certain amount of time passes and I don't feel any closer to finding a workable solution, I'll skip the level altogether and come back to it later.
I very rarely spend more than about 20 minutes on one level, and even then it's only if it's a compelling enough level that I feel very close to actually solving; as you've said, lack of fiddliness can be a good indicator that the solution you're trying is intended, so if I'm onto a non-fiddly solution that's only a few assignments away from being solved, I'll persevere. Otherwise, if I can only find hackish stuff that isn't working, I'll happily move on.
Keep red herrings that work 70 % or 80 % and have to be executed first to see why they fail. These dead ends are still honeypots, but fail much more clearly than the 99 % red herrings. That's good entropy, it feels like getting stumped fairly.
Yes, definitely. This is a good rule of thumb that responds well to the OP. Combine this with Icho's (and my own) suggestion of moving the difficulty scale and it's a recipe for a better player experience
Just remember that players have different styles as well as different abilities, and it's almost impossible to guess how any player will approach your level.
The more inclusive you can be of this, the better your levels will be.
See
this thread on difficulty ratings for related discussion
