For a very long time the UK has proceeded down the road of closer relationship with Europe and for too long the people weren’t asked what they thought about it.
The UK has proceeded down loads of roads over the last 40 years without asking the people in a referendum. Privatised quite a few industries. Banned smoking in workplaces. Introduced the minimum wage. Restricted trades union powers. All of those have a huge effect on many people's lives. What makes the relationship with Europe so different that that uniquely justifies a referendum?
It is quite simple - if you have a referendum and say you will implement what the people decide, you need to do just that I’m afraid. The consequences of yet again ignoring what people think - the common wisdom of the common man if you will - for technocracy and an insistence the political classes know better, are dire.
Even aside from the controversies over various lies etc., that logic only really works if the referendum offered a choice between two well-defined and easily implementable actions. It didn't. The referendum offered a choice between one choice (leave things as they are) and another choice that was almost completely undefined. As I've said before, it was a bit like having a vote on 'should we move house, or stay in our current house?' without giving any idea of where we'd move to if we did move. In that situation, if it takes the Government 3 years to work out a place to move to and in many ways that place looks a lot less favourable than the options that were being speculated on at the time of the vote, then I think most reasonable people would say that it would be daft not to hold an additional vote to check whether people really did want to move to this new place.
To some extent I agree with you that damage has been done to democracy. But that damage was done in 2016 by holding a referendum on something that was so vague as to be virtually undeliverable in any form that would satisfy most people who voted for it, accompanied by an equally undeliverable promise by the Government.
To my mind, it's time to accept that the damage has already been done by holding that flawed referendum, and do what we can to minimise that damage. And it seems to me the least bad way to do that is to hold another referendum that is properly framed with two clear and well defined choices.