Deputy immunity gives the legal right not to obey any requirements of any authorities, except by a court decision. So if you are a drug addict, then a deputy is a very convenient position for you.
I don't think they need such supervision. These are Orthodox people of the highest morality, who do not take care of themselves and are engaged in arduous intellectual work in conditions of non-covetousness and faith in a bright future. They do not take care of themselves at all and think about Russia, golden people!
Since April 1, you, Russians!
Counter question: who is watching the sellers, janitors, managers, lawyers, cooks, programmers, doctors, zoologists, teachers, etc.? ...
The question was raised from the wrong side, of course no one is watching :) Because the deputies in the Russian Federation are an inviolable elite who wanted to chhat on laws for cattle.