Brexit is also unusual, as others have alluded to, in how skewed the demographics were by age, which is pretty significant if the repercussions are expected to last for a decade and affect the proportion of the public too young to vote significantly more than the proportion of the public most significantly in favour of Brexit.
The other side of that argument is that the referendum saw an unusually high turnout for a UK election and the margin as wide as those which have produced comfortable Parliamentary majorities. On the other hand, more people voted against Brexit than for any party that ever governed the UK by itself.
As for alternatives, I mentioned higher quorums ("If 50% of the entire electorate vote Leave, we'll leave" would have seen no change happen, at least until Cameron was undermined by his own party) which are actually pretty common for major changes in democratic votes within organizations. There were also calls for 16/17 year olds to vote although this certainly wouldn't have affected the end result.
Tangential point for futile rhetorical arguments: the split between net taxpayers vs net recipients of state benefits/pensions which I don't think any pollster has been bold enough to evaluate. Usually pensioners are strongly conservative and the unemployed and unskilled part-time workers strongly left-wing which makes "our voters are the ones paying for it" arguments redundant, but Brexit is one cause that almost certainly united the votes of pensioners and the unemployed and underemployed, and depended on them to prevail
https://en.wikipedia.org/wiki/United_Kingdom_European_Commun...
...do you think there should have been a referendum on the Maastricht Treaty?
Although that immediately raises the question of whether a vote to remain was really a vote for the status quo in any meaningful sense. What if it was interpreted as, for example, giving an active mandate for the "ever closer union" advocated by many European politicians? What if the UK found its negotiating position within the EU weakened once the long-standing threat of leaving had passed?
As we're now seeing, the in/out status alone is only a very small part of the story.