Regarding the bolded bit... well, it's their job - that's quite literally the sole reason we elect them. Sure, they will make mistakes, but we effectively hire them to not deliberately make those mistakes and act in good faith.
Now here's the problem - the vast majority of MPs privately believe Brexit is utter madness. If they had a free vote now on it and it was secret and anonymous, they'd vote against Brexit everytime.
As for "responsibility was passed from the government to the voters", that is simply not true. Here's the actual black and white:
It was always meant to be advisory. Yes, it can be a strong influence, but under no circumstances can a non-binary referendum be used by politicians to excuse them from doing their job.