I posed my question for the OP, and despite them responding to the thread it has not been answered.
(For the record, there are motorways, some Plazas, Private Property and precious few other places where it is illegal for me to take my bike).
Given that the CF is some 800+km long, with numerous variants, encompassing everything from single person wide rocky trails to urban areas and stretches along main roads, I am bemused by the notion of a single "bicyclists should take to the roads" assertion. My first question would be "what constitutes a road?"
That is not a smartass question.
If it is legal to cycle on the Camino the question then, is less about bikes and more about the people on those bikes.
That brings us to the nub of the issue, in my opinion - the behaviour of
people.
As someone who rides a bike I find it offensive that someone thinks it is perfectly alright to suggest to me where I can ride that bike, not based on
my behaviour, but on the behaviour of
others.
Here's another smartass question. Do we have any stats on injuries caused by cyclists to Pilgrims on the Camino?
I am not trying to play it down in any way but I believe that regulation (enforced and self) is most effective when based on reality and not perception.
Speaking of perception, fear is a perception. This forum is full of people posting directly or indirectly about their fears and making decisions based on them. Just because someone is afraid of bikes is no more a reason to advocate for their removal than it would be to advocate for the removal of dogs as just one example.
The harm that bikes can do to some trails is a hot topic in some countries at the moment but I'm not aware of any controversy in Spain.
In all honesty, given the ever increasing numbers of Pilgrims it's far likely that pedestrian traffic is doing the most harm.
I'd be wary of introducing environmental issues as an argument for discriminating against bikes what with lots of international air travel and baggage hauling as common topics on these fora.
I'm waiting, with interest, to see the development of a "Green" Camino movement.
My personal theory, is that there is too much "them and us" in any debate that involves cyclists. Interestingly, that debate seems to be very much centred on the English speaking world, and ironically, is not something that is prominent in Spain amongst the Spanish.
Drivers hate cyclists. Pedestrians hate cyclists. I ride a bike. I drive. I walk. I must really hate myself!

Seriously, though, such discrimination is a serious problem, especially when people bring their own perceptions and understandings to Spain (and Portugal) from foreign places.
Even the title of this thread is simply "Cyclists". How many people opened this thread expecting it to be a happy, joyful thread about the wonderful people to be met who ride bikes?
I find the idea that because I have a bicycle, it's acceptable to be told that it would be appreciated if I take to the roads chilling. It is the first step on a journey that brings us to unpleasant places.
Who is next to be discouraged from following a Camino? Those on group tours? Those who use baggage services? Non Christians?
In a general sense, there is no shortage of evidence, of anti cycling behaviour on the roads of certain countries, flames fanned, I believe, by notions such as this.
I have no problem at all (and have posted here before on the very topic) of introducing guidelines for both people on bikes
and people on foot as well as devising rules and laws. Where, I do have a problem, however, is people deciding what I can and can't do (and where I can do it) based on
their personal preferences.
Anyways, at the very end of this discussion it has to be faced that anyone advocating for what can and can't be done on a Camino is most likely a foreigner dictating to locals what they can and can't do.
I can't think of too many places in the world where that approach will go down well.
As with most things to do with planning a Camino I suggest strongly that we leave a lot of mental baggage at home and make the best of what is in front of us. How many of us planning a weekend away would scour for information on the best hotel to stay in are happy and grateful to wander up to a small village and take a bunk in a shared dorm?