Yet one rope can hold all that weight...
And I could propose slight variations on the mechanism which would not require the weight of the stone cube to be supported by the rope, but which would still meet the 'player experience' of the trap...
I think this all illustrates that, for most anything but basic forms of trap which are well known in the real world, it is debatable if such a mechanism would seem reasonable to EVERYONE at the table. I think the same can be said of a great deal of fiction in a D&D game. One must thus put aside some amount of skepticism and replace it with an attitude which I would call more 'scientific' and 'experimental'. That is to say to yourself "I'm not sure about this, maybe its ridiculous, I can think of objections, but I'm also seeing it and thus need to take it seriously." This is a form of suspension of disbelief. You can still reason about things, but you need to use a bit different logic. Instead of using your critical 'engineering hat' and trying to find all the reasons something might not work, use your 'dm hat' and think about what might make a plausible trap scenario in a dungeon full of monsters. It doesn't have to have every single loose end tied up. Nobody ever explains how the monsters on level 2 manage to get food and such, they just do. This is a given.
With that understanding, I do think traps like this are perfectly fine puzzles. They reward cleverness and punish thoughtless short-sighted action by players who either are not using their wits, or who are being overly pedantic and trying to engineer everything. OTOH if a player were to say "well, if trap X works like Y, then there must be a way to reset it, Z. I'm looking for that tool/mechanism/fixture." Maybe the DM didn't think about that, but it would be reasonable to say "OK, sure, its over there on the wall." A lot of 4e traps spell out mechanisms which allow them to be bypassed if you look for them, and there's no reason classic traps cannot do that too. Just saying "yeah, there's a plank propped against the wall to the left of the door." would be a bit of a reasonable clue in this case. It won't reveal the workings of the trap, but it allows for a perfectly sufficient way to bypass it that is plausible (and maybe the plank is on the other side, someone will have to cross).
Honestly, the beauty of this trap is that it isn't just some trapped door "when you open this you get hit with 3 poison darts, make a save" or something like that, which is really pointless and just leads to pixel bitching the whole dungeon. Granted, it is a bit more plausible sort of trap, to a degree, but meh. I prefer interesting play over some sort of faux 'logic' for things that are already vastly illogical to start with.