Flawed scheme as it does nothing for the self employed.
The scheme was never designed, it came out of some clever combining of some existing rules. This meant that HMRC could sanction it as a legitimate tax avoidance without any changes to the law. IIRC the existing rules include the Green Travel Plan (which allowed companies to provide employee buses and/or a bank of bikes for employees to borrow) and the salary sacrifice rules, plus the rules on write-down of capital expenditure.
Pure self-employed can't get it as they don't fit the employer/employee model for those rules, but self-employed as a one-person company can, and arguably they are a more pure fit to the rules than the finance schemes that have sprung up.
It also doesn't help that HMRC changes the rules last year, restricting the scope of Cycle to Work (so if you work from home you are no longer eligible to use the Scheme, whereas you had been previously).
Well that's hardly surprising as the point is to allow you to cycle to work. Unless you want to argue at an HMRC tribunal that you really are using the bike to get from your kitchen to your study.
Or the retired or unemployed.
Or this for the same reason. Its tax avoidance allowed for the purpose of greening travel to work.
The point about the low-paid is a valid one. There's a gap between not paying any tax to avoid, and earning enough to pay tax but not enough to be able to salary sacrifice. This is for the reason given above, without the will to create actual law and devise a scheme from the ground up, it's simply a mangling of existing rules that were never originally intended for this.
And the point about specialist bikes is also very valid. But that's an issue with employers who are unwilling to accommodate and will only allow employees to use a specific finance provider (aka scheme). There may be scope for action on that point by arguing the scheme they offer is not equal for all employees, but I imagine the result of that would likely be withdrawal of the scheme entirely by that employer.