there is no reason in the world why a bunch of unqualified, elderly misogynistic mystics should be any part of a modern state

Unqualifed: The Archbishop of Canterbury has a Cambridge degree and 11 years in industry before being ordained.

Elderly: Experience often increases with age. Are you being ageist ?

Misogynistic: Most bishops have wives and it was not them who were blocking women joining their number (http://www.bbc.co.uk/news/uk-18702908)

Mystic: person who seeks by contemplation and self-surrender to attain unity with the Deity or the absolute, and so reach truths beyond human understanding. Not my cup of tea or that of many here, but an awful lot more than 1 in 10 of the UK population have some respect for that (statistics in a recent discussion, can't be bothered to check them).

No reason in the world: even if they were what you say the reason is that politicians we vote for have not agreed to change the situation. Sour grapes that they are not the politcians you voted for is part of any modern state.