Houseboats are not something you see on that sort of the network, I think you mean narrowboaters.
Whatever. This isn't canalchat so it's not surprising I'm not jargon-compliant. How about answering the substance of the question rather than nitpicking the use of a wrong word? Surely any bit of live towpath may have some legitimate reasons for cycle access?
There are some parts of the network where cycling isn't compatible with other users of the towpath, and in those cases it's better that cyclists are prevented from using the towpath on that section of the network. It's no different to prohibitions on fishing (various local rules), mooring (see the 1995 Waterways Act and various bits of local legislation), the towpath being closed to everyone for stoppages, or preventing cycling in pedestrian zones in town centres.
Whereas I'd say in those cases it's better that the towpath is upgraded to be fit for purpose, especially when they've taken more than some whole county's cycling budget to improve access to one towpath.
I don't agree that it's identical to prohibitions on fishing, mooring or stoppage closures. It's more like preventing cycling in pedestrian zones in town centres, which is usually amazingly wrongheaded, commercially harmful, done contrary to the guidance (for the last 35 years in the case of pedestrian zones) and ignores it being allowed in most neighbouring countries.
Why? That line doesn't sound so different to a Daily Mail type motorist screaming "I pay my road tax!".
How? Road tax hasn't existed for ages, whereas the towpath improvement funding clearly did! The partnership accepted funding to "provide people travelling on foot or by bike through the valley with a safe, scenic, traffic-free route they can use all year round" (according to quotes in the link posted earlier). If they're not going to deliver that after all, the bulk of the funding should be spent elsewhere towards that aim.
Some boaters are just as badly behaved as all the other groups, by the way. A lot of liveaboards sneer at the the IWA calling them the "shiny boat brigade", but if groups like the IWA hadn't campaigned and indeed put their own labour into rebuilding the derelict canals in the 1970s, there wouldn't be a network for people to claim ownership of today.
You know more about boater bad behaviour than me. I've not had any problems riding CRT towpaths in Somerset, London and mid-Lincolnshire, but I don't get there that often now. The fens waterways seem to be mostly under the control of the Environment Agency or Internal Drainage Board.
Thanks to those who rebuilt the derelict canals, but surely that shows that canals can and should still change to be relevant to current needs and desires, not have mistakes kept as museum pieces when they harm current use.
TL; DR: we don't know the reasons some things are done in the way they are. Maybe the reasons are historic, or maybe there's another insight none of us have as we weren't involved in the decision making.
Then I feel it's up to those making the decisions to explain them to the public when public money is involved. I don't think knee-jerk defences of what looks like misspent public funds is good for anyone.