Nice idea, but the problem is that not only do people get very few tax breaks for cycling, but they get much more for driving cars. Especially in the UK, almost every manager is given a free company car because the companies pay hardly any tax on them. Here in Switzerland the subsidy for driving cars is more subtle but just as effective.
People can deduct generous allowances for driving cars, but little or nothing for cycling.
I'm happy to discuss anything further with anyone in private emails though.