The problem with Brexit is not necessarily just whether or not Brexit had happened, but the fact that after the referendum, there was a supposed "popular mandate" of implementing Brexit, but nobody could say what exactly that mandate was since the people didn't vote on a particular proposal, but only on a vague idea. This led to the downfall of not one, but two governments, and it would have nearly triggered a constitutional crisis.
By contrast, if there hadn't been a referendum, either the MPs would have agreed on a specific Brexit proposal, with everyone exactly knowing what they were getting into, or they wouldn't have been able to reach any consensus and would have remained in the EU (similar to how the Trump administration couldn't repeal Obamacare because nobody could agree on the alternative), both of which to me seem preferable than the mess which Brain had to endure for years after the referendum.
Also, it's not necessarily just the fact that MPs are intellectually superior than the rest of the population (although I do think that, generally, the dumbest of the dumbest make it into parliaments somewhat more rarely), but the fact that parliamentarism and the associated procedures, laws and standards has some checks and balances built-in that pure mob rule (in the most extreme of versions) doesn't.
(and as a final remark: I'm not generally opposed to any sort of plebiscite. I'm just saying that there are definitive drawbacks to direct democracy - you can see that even in Switzerland, where the system is generally much better thought out and established than in the case of the rushed Brexit referendum - that you need to prepare for, and you shouldn't just say "the will of the people counts" because there are huge pitfalls in trying to figure out what "the will of the people" even is (see: basically every populist government, and/or politician in world history, there are even examples of this dating as far back as the Roman Republic)).