It won't, you haven't cut any hierarchy, that's not how the EU works (but the UK let themselves get disinformed about that for decades by certain Mr. Johnson and others). A citizen can meet the politician in the supermarket in the same way as before and it does not matter, because the politician lied to him, the citizen believed him and voted for the Brexit and nothing got better. Now the citizen does not believe in democracy in general. Trust is what has been lost.

I can meet my MEP in the supermarket. I can write to him an email and he will reply personally. This is a non-issue.