I've voted for yes but accept a sort of halfway house, i.e. it's complicated. Firstly, even as a cyclist but not a commuter, I think that only folding cycles should be allowed on peak services into cities/large towns where there is a major commuter flow. Generally on routes with services to meet that kind of demand, there is a finite capacity determined by the trains and/or the infrastructure, and given that the level of cycling is on the increase, there is not much chance of the necessary capacity being available in time for that increase. Equally, push-chairs should also be foldable and folded in the peak because if there isn't room for cycles then there isn't for them either.
On regional, country, long-distance services and commuter trains between the peaks, provision for full sized solo cycles should be based on some measure of meeting the demand, but I imagine that it would take some time for provisioning to catch up with that, except of very high capacity commuter train designs such as class 700s and 345s.
In the case of conflicts, cyclists and non-folded push chairs should be able to buy tickets for their wheeled aids, and in that case, a ticket holder would have priority over a non-ticket holder. If both do (or both don't) hold tickets, then it's first come first served.