I thought your argument was that VAT shouldn't be charged on cycles because people would use them to commute on, with environmental benefits over driving to work or using public transport.
A Focus Cayo might used for 'pootling' around local routes would have no environmental benefits because this is not something you do by bike rather than car.
If your argument is rather that VAT shouldn't be charged on cycles as sports equipment because of health/obesity issues, then equally it shouldn't be charged on other sports equipment like golf clubs, canoes, hang gliders, fishing rods, etc ?
I dunno. I'm in favour of VAT being charged on luxury items - which I regard a £1000 bicycle as.
Most people commuting short distances to work could do it on a £200 bike.
Similarly most people taking-up cycling for exercise could equally do it on a cheaper bike.
I can see an argument for not having VAT on cheaper bikes used for these puposes, but when you get to spending £1000 on a bike it becomes a luxury item, the sort of thing cycling enthusiasts lust after.
It's no longer a utilitarian device, no longer a machine for getting to work or working-off some flab, it's now a plaything for the sort of people who can afford £1000 bikes - and if they can afford that, they should be paying VAT...