"Is the prevalent feeling that the public can consider themselves lucky to choose between candidates, who more often than not went to the same elitist schools, depicted and promoted by media run by their former classmates?"
That explains the antipathy towards the young (in particular) to politics. However it also explains the even greater antipathy towards Europe.
The EU appears to be run by a bunch of political has-beens (Neil Kinnock anyone?) who gain their positions and substantial salaries purely by means of their connection to the old politicians club. There was certainly no democratic input into that process.
I think it is easy to support the general EU objectives of free movement of goods, services and people. But it is very hard to support the opaque and incestuous political structures which underpin it, and which we can do nothing to change.