What kind of worrying implications does it have I'd the parlament does it job? Members of a parlament are for a reason not bound to anything except the own conscience. It's an additional safety measure in a working democracy.
The strong elements of direct democracy in Switzerland wouldn't work without a strong parlament.
Its more to do with democracy as understood by the layman in the modern day - namely, that the will of the people is understood as paramount. A government that actively decides to ignore the wishes of the population is a government that's going to get a lot of flak, especially one for a nation that put itself front and centre in the whole mess of 'building democracy' in regions like the middle east.
But as you say, that's part of the point. Majority rule isn't always rule of the smart or the just, and most people don't have the qualifications to make a decision regarding international politics. On the other hand I would equally say that many of the people currently nominated to do the job
also lack such qualifications, but then that's a problem with regards to how and why they're put into such positions to begin with (oh party politics).
Thinking on it, I suppose part of the particular problem right now is that Cameron's resignation, while a brilliant move in ensuring Boris Johnson was going to be screwed over
somehow, also places a greater impetus than usual upon their successor - in this case, May - to actually act upon the vote. After all, they got to be Prime Minister
because of Brexit, and from the perspectives of many, that's all they're there to do. While I suspect from May's perspective, she may find it to ultimately be the only way to solidly legitimise her position, since she's refusing a General Election, and the vote to make her the Conservative leader never went to the member base. Thus the only way she can currently be seen to have a democratic basis to her position is to follow the referendum result.
