I think you are confused. Cycle to work does not equal cyclescheme.
Cyclescheme is an organisation who were setup to provide an administrative service to organisations who wished to provide a cycle to work scheme to their employees but didn't want the administrative burden of drawing up the hire documents and dealing with the bike shops. They are often referred to as facilitators.
For the Department of Transports guidance on Cycle to Work then I suggest you read this.
http://www.dft.gov.uk/pgr/sustainable/cycling/cycletoworkschemeimplementat5732?page=1#a1021
The organisation bought the bike and then hired it to the employee. At the end of the hire period the organisation can dispose of the bike and if they dispose of it to the employee there are certain regulations regarding that sale one of which surrounds the proper valuation of the bike. If the bike has a value and is owned by the organisation (otherwise how can it sell it) then that is what is called an asset or at least it was when I done my degree. Can you explain how its not so.
I think you have used existing knowledge of taxation to form an opinion as to why an organisation would hire the bike when in fact the reason for hiring is because the 1999 Finance Act expressly permitted huge tax savings to be made in order to enourage a greener form of transport and to help employees lead healthier lives. That's the reason why so employees have lobbied their organisations to introduce this scheme. Its nothing to do with the rules around the capitalisation of assets.