This is just conjecture and assumption.
To some degree, but I do know some people who voted for Brexit and I can tell you they very much didn't want to stay in the single market, with all that entails for regulation, for example.
As for the customs union, I don't think 99.9% of people knew what that was or even heard of it before the referendum.
This would have been the obvious compromise position, have Brexit, so you can make the "respect the referendum result" claim (despite the misgivings about the referendum many have, see above), but don't have all the restrictions and difficulties Hard Brexit entails.
Any approach has difficulty though. Would we have even been allowed into EFTA, for example? There were conflicting reports at the time. Certainly unless we were serious and enthusiastic about it, it didn't appear it would have happened.
And why should the Hard Brexiters be allowed to have their way on a marginal 52% result, while the Remainers have been completely and utterly ignored with no consideration of their views whatsoever made?
That's a problem with referenda, particularly one that ends up close. I'd strongly agree that 'leave' should have been defined before the referendum, but as it wasn't then we are where we are and people were free to define leave as whatever they felt like.
I'd add that it *was* strongly hinted that leave would mean leaving the single market and customs union. I've debated this before with a 'hard' Brexiteer when I was supporting 'Norway' and at the time I was arguing that this wasn't the case - but he showed me more than enough interviews and articles from 2016 that I had to admit I was wrong, and that was indeed strongly implied, at least by many in the leave campaign.
But in this case, the whole thing is just so unnecessary. There was a simple solution, remaining in the customs union. Like we have done throughout modern times. Then the whole NI question would never have arisen.
I posted an article yesterday (by someone who seems to understand these issues better than me) that argued that wouldn't be sufficient, you need to be in the single market as well. I know Labour were arguing for this as a possible solution throughout 2019, but in retrospect I think they were wrong.