The non binding referendum was pretty close, you sure the other half of the population doesn't already feel that way, as in the system sucks, then this shit passed, thus confirming the system sucks?
It just seems your logic applies to both groups considering your starting point. And now the leave side is smaller so one could imagine there are more disaffected people in remain now, if your prerogative is simply to make the most people feel best about the system shouldn't you be open to another vote?
Overall it just feels like your statement really only stands if you only look at leavers that way and ignore the stayers since you established the system sucks going into it and everyone's disillusioned.