If you are a Brexiter and pleased with the outcome, perhaps you could consider how you would have reacted had the outcome been 52:48 the other way ... quietly accepted it and said "Fine, that's it for another 40 years or more"?
I think not. I think the outcome that would have followed had the vote been 52:48 for remain is the outcome that should have been followed given that the outcome was 52:48 for Brexit.
Which is: wow, that was a close result, there is clearly antipathy towards Europe, let's take that back to Europe, give them a chance to improve the things which we all know are wrong, and have another referendum in 2 or 3 years when we see what they come up with.
I have to say, I don't think they would have done much (much as they didn't when Cameron went out there early in 2015) and that second referendum would probably have resulted in a bigger Brexit vote - but who knows?
"Improve the things which we all know are wrong", while keeping the bits that are in the UK's best interest, is the ideal outcome for David Davis. i.e. we don't remain in the EU, but we end up with a relationship which is the one that we would have wanted with the EU anyway. Bloomberg's "Europe's Ties That Bind" Euler diagram perfectly lays out the size of the economies and the relationships between various countries in the Euro, the EU, the EEA and EFTA:
https://assets.bwbx.io/images/users/iqjWHBFdfxIU/iNllUULaAcYA/v2/800x-1.png
Davis needs to figure out where we fit in a new version of that diagram.