Your point about "legally binding" elections is irrelevant: Parliament can legislate in whichever way it chooses, including, if it so chose, to invalidate the result of referenda which it had previously declared to be legally binding. It also possesses the power to legislate away general elections if it wanted. The democratic relationship between parliament and the electorate is based fundamentally on convention and trust.
There were not a "large number of reported improprieties" reported during the referendum, but even if there had been, these were overcome by parliament's acknowledgement of the legitimacy of the result first via the Withdrawal Act and second via the manifesto pledges of the Conservative and Labour Parties in the 2017 general election. Your vague argument about "the events leading to the referendum happening in the first place" is similarly baseless given the overwhelming assent that parliament provided the Referendum Act in 2015. So "the point is" that if successive parliaments, prime ministers and opposition leaders, after having unambiguously led the country to believe, both through words and legislative acts, that they would honour the result of the most important constitutional referendum of a generation, then turned around and ignored it, that would annihilate public trust in the democratic institutions.The public trust argument is also shaky at best, considering the large number of reported improprieties during the referendum campaign and the extreme polarization of the British public that followed. I would argue the events leading to the referendum happening in the first place and the way it did happen, laid the grounds for the erosion of public trust. The point is, the UK is already there and if there was the will then a second referendum could become morally viable, or at least morally viable as the first one was.