I decline to derail this with my own views on Brexit itself, but in answer to your question on what would have happened, I think if it was up to the government they would have bumbled along with one foot in the EU door much like before (not joining the Euro/Schengen, special conditions for the UK) which from outside might be seen as a reasonable compromise between the different factions of the UK.

I used to be in favour of direct democracy btw and somewhat changed my mind lately. The 2019 Reith lectures may have something to do with it - Sumption raised quite a lot of points I hadn't thought of before, in particular making a link between direct democracy and our lawyer-up culture of everyone-suing-everyone-else-all-the-time (the linking factor being the appropriate role of judges in society). I think he would also say it's the first past the post system that has caused so much alienation from the political process (when so many have votes that don't count), rather than there being a problem with representative democracy per se. Worth a listen (also on any podcast app): https://www.bbc.co.uk/programmes/m00057m9/episodes/player

I would add that there's a bunch of other issues that caused that alienation, not least mainstream economics being so far divorced from reality for so long; also our media is a disgrace (not that I have any ideas for fixing it I'm afraid).

So would it have happened if we had direct democracy beforehand? I don't know, but I reckon we'd have replaced one problem with another one generating just as much discontent.

Sorry I had missed your context on local issues, you are right about the EU being abstract to most people, though there will always be issues in trying to draw a line between local and global.