I am in favour of compulsory reservations for cycles on all trains (even local ones) due to the limited resource that is available. However, I would make them available much more widely - so they would be available, independently of a travel ticket, at ticket offices, at TVMs and online via a dedicated website and app as well as compulsorily offered (and visible on the search if they are available or not, or via an option "only show me trains on which I can take my bicycle and space is presently available") when booking online at all booking sites.
I would charge a fee, but only a nominal reservation fee to discourage people from frivolously booking on all the trains they may want rather than the one they do (a bit like £0.05 for a PERTIS stops them all getting dumped on the floor by the local scallies). £2 to reserve but £1 refunded if cancelled/changed in advance of departure would seem a sensible sum and is the same as I support for seat reservations. After all, the cycle brings other (fares) income; there are few journeys where bringing the bike is an optional matter, mostly either a journey with a bike makes sense or it does not, and if it does make sense without one isn't a sensible option so the ticket income is lost.
Ideally, guards (where provided) would have an easy facility via their phone to release them if unclaimed from the specified departure station.
Because of the lack of need to mark them (as they are compulsory) they would be available, as they are on VTWC, near enough right up to departure. A long advance booking requirement like TPE's inadequate scheme is not acceptable nor necessary.