I served as an independent member of a police authority for four years. It was an interesting experience and I think was worthwhile, although the reliance on the same organisation one is meant to be 'critical friend' to for one's information does limit effectiveness.
The selection process isn't ideal, although it is quite exacting. I applied twice and was successful on second application after quite a gruelling interview process. As an independent member with experience of being part of a minority community, I felt I had some distinctive perspectives to bring. The problem was that it was very hard to remain independent. I declared that I knew the Chair of the authority, and whilst for the first two years of serving I was a party member, never felt any loyalty to that party's position. This was probably my downfall, particularly when I left the party and it became pretty clear that I wouldn't be reappointed.
However, further politicisation of the police via direct elections would be a very bad idea - and I think would undermine the authority of the Chief Constable. It would mean that police governance would be in the hands of one party, and this could easily be an extremist party unwilling to enforce the very important commitment of the Police to serve the whole community.
There are other ways of enabling people to influence the police without placing them further into the hands of party politicians of any colour.