This is why major changes to the fabric of a country are usually required to pass a far higher hurdle than merely 50% of the voters. You need a convincing margin to persuade those voting for the status quo to accept that the will of the people really has changed and that this is not a statistical blip fed by lies. Nobody is at all convinced that a second referendum, even at 50/50, would yield the same result now that the horrendous lies the leave campaign made have been exposed for what they were which happened within hours of the win.
So let's not talk about what should have happened (and I do agree with your arguments in their entirety, btw). Let's talk about what did happen.
The entire things seemed to be a farce, with no real plan of how to enact an exit because the idea that BREXIT might happen seemed so far-fetched. The bar was set as "50% + 1", but with nothing to make this a binding referendum. The expectation must have been to vote to remain by a huge margin, because now you have the reality of Parliament being able to ignore the will of the people, even though they agreed to this in the first place.
If this was proposed as a script on "Yes, Prime Minister", I doubt it would have made the cut.
Because of this botched process, you now have the possibility of the UK staying in the EU after a majority of people just said they want nothing to do with the EU, or actually leaving the EU because the process was treated as a joke. If the UK stays, it just made a mockery of the referendum process; if it leaves, it made a mockery of the democratic process (the excluded voters you mentioned).
Surely the UK learned that appeasement was a bad idea in the 1930's. Trying to appease Nigel Farage appears to have backfired as well.
Either way, there is a lot to learn from all of this.