While i agree with your sentiment over the pro rata for all to encourage people to come back within this membership year, i don't agree with the below statement.
Competitive archers already pay more, and I feel you are just looking at the small picture and focussing on an individual's club only. Competitive archers are a huge benefit to the archery ecosystem.
They tend to buy the big ticket items at shops aiding in keeping them afloat, alongside the stream of beginner and intermediate kit. Many actively promote certain shops and the sport itself. They pay up entry fees at competitions hosted by various clubs, which in turn funds other clubs coffers which leads to membership fees for those being kept fairly low.
Example being, my previous club (member base of just under 50), based on school grounds, didn't/couldn't run open competitions, membership cost circa £350pa (inc. AGB/County/Region). My current club (member base currently around 80, usually 100+), based on own field with clubhouse, runs or hosts several open competitions over the year, membership cost circa £150pa.
See without the income from the competitive archers, membership cost to the club itself would be more restrictive and could become akin to the likes of Golf Membership fees.
At the end of the day, how much a person shoots is entirely decided by them and (basing this purely on AGB membership fee), what else can you do for less then £4 a week?