Yes and no

It seems to me, however, just using logic and reading about what law enforcement can and does do in catching on-line child pornography users, that it must be possible to prevent any child porn sites from using the Internet. It must be possible to block such use so that no one may access child porn sites. Then no one could ever be arrested or prosecuted for possession of child porn.

Ergo, it seems to me that law enforcement is purposefully allowing child porn sites on the Internet. This to build up their image in the eyes of child sex crazy societies, viz., the United States of Amerika. And when they build up their image, they can get more money. And when they get more money they can hire more criminals with badges...er, officers.

If you speak only about websites, ie, pages or sets of pages sent through an HTTP or HTTPS protocol from one computer to another, and on the public internet, (something like www.clickhereforkiddiepronz.com) then yes, you are right. And yes, any such website is a honeypot.

[Caveat: laws are not identical from one jurisdicton to the next, so there is still some small but non-zero chance that you find a site in country X giving you materials which are illegal in your own country and which is not a honeypot. This is how the Kiev studios worked, for instance. That said, minors having explicit sex with adults or other minors is, afaik, illegal everywhere, so this caveat only applies to things for which there really is a difference, such as cartoons and drawings, clothed but sexy pics, or naked but not having-sex pics.]

But the thing is, that is far from the only way anyone can transmit stuff over the internet.

Some sites are ostensibly on the public internet but are password protected. All social sites, and probably all, but at least many, media hosting sites, allow you to password protect access to content. Suppose you have an account on MyBook, upload KP to it, but put it under "share with friends only". Then it's usually not accessible to anyone but people you already appproved. This allows diffusion. Of course, if anyone reports it, it will be down and you will be arrested, but it gives anyone enough of a window of time so that it's not as easy as you make it sound. Most such sites claim that they watch everything that they get uploaded, but I don't think it is a likely claim for the biggest sites.

File sharing sites such as RapidBox allow you to put a file on them for public download. You can then use them to put a zip'ed or rar'ed file containing hundreds of smaller files. You can even password protect that zip or rar so it cannot be caught in case the site monitors what is uploaded or someone downloads it by accident. About the same as the previous: anyone reports and you are down.

And that was the easy part.

Do you know about email? What about IM?
Anyone can transmit KP over email or IM, and it is not visible to others unless there is someone already listening to your transmissions.

Do you know about P2P (the old Napster)? What about the Pirate Bay (and torrents)?
True, both work under the assumption that your IP address is visible, so they are extremely easy for others to catch you (which is the premise of how they catch media pirates too). But in both cases, you can transmit a file to others for some time. In both cases, your being caught will have implied that someone got the file who either was police or showed it to police, or that you received it from police, not a KP owning civilian.

And from here, it gets even harder.

Someone realized that P2P/Torrent technology lacked an anonymous way to do it. They invented Freenet.

Someone realized that the very website structure lacked an anonymous way to do it. They invented the protocols that go as .onion and I2P. In both these models, the website is hosted, all encrypted, in a server that is somewhere (about anywhere) but connects to the internet only through Tor. This means that it never knows who it is communicating with or their real location, and also that whoever access it cannot know its location either. This means that even if police knew the sites, it cannot bring them down. In principle - of course, in real life it might be able to; but that is more because of the weaker link of humans than because of the technical aspects.
And this is relevant because recently hacked (or at least attacked) Lolita City was a site hosted under one of these protocols. Supposing the site is really illegal (and not merely controversial, which could be GC too), if it is behind Tor it is still impossible to know where it is. Whatever Anonymous, or police, do, they cannot really bring it down permanently, or at least not by the procedure of finding and arresting the site owners. And even if it were a honeypot, being behind Tor works both ways, so the site does not know who the users are. It would still be useful to have a honeypot set up that way because users could always post stuff about themselves; but it would not catch all users, but only a tiny minority.

So, summarizing:

Yes, any open internet website which has actually illegal KP is a honeypot.

That doesn't mean that the internet cannot be used to transmit KP without police detection.
That doesn't mean that all such transmissions are known to police or have police at one end.
That doesn't mean that there cannot be websites on the hidden internet with KP, and which are not honeypots.

So, although the claims of police about KP on the open internet through normal websites are ludicrous, they could be at least a little less ludicrous if referring to other protocols or to the hidden internet.