the amount of nepotism and corruption involved in being able to get one
this is a pile of shit and you know it - the public sector is THE place where there are clear and transparent HR policies, including for recruitment, which is undoubtedly why there are more women represented in the workforce as, for example, overt discrimination against women of child-bearing age is not allowed. If you have actual evidence of corrupt practices (you know, something you could prove, not just something your friend's cousin's neighbour heard about) then you should be raising that with your local councillor or MP because that is of concern to all tax-payers. And just to submit some anecdotal evidence of my own, the only examples of nepotism I know of have occurred in the private sector.
many people end up feeling like banging their head against the wall after having to deal with some of the pig-ignorant people that work in local councils in particular
In particular? You mean that people who have dealings with, say, Ryanair, utility companies, banks, insurance companies, phone companies, etc, etc, do not come across pig-ignorant, lazy, incompetent jobsworths? I don't think so.
Human beings with all their numerous faults work in the public sector. Human beings with all their numerous faults work in the private sector. The only difference is that because the public sector is forced to be transparent in its operations, you get to hear more about about its failings. The exact same criticisms that are levelled at the public sector can also be levelled at the private sector.