Well, I'm not a vet, I can only speak to my personal experience. It's worked very well for me, and not in a single case have I personally seen it make things worse. Equine vets still use it (at least those that know about it). This article I linked to earlier, is a bit humorous, but by vets:
https://www.americanfarriers.com/ar...-mess-that-works-when-treating-wound-injuries
Doesn't mean that for someone, somewhere, maybe there was a different result.
Since you have seen improvement, I would not consider that it's hurting anything, and probably helping. When I stop is when I see healing going on, no pus formation for a while, nothing but healthy looking tissue. If it's a deep hole I make sure that it's healing enough from the inside before stopping so that it doesn't heal on the surface first and close any bacteria in.
I will not be critical of a profession that I don't have a license in, but my experience over the years is that many simply do not know. They are book taught in schools that are subsidized by pharma, so......
Not slamming pharma, some of what they do is pretty valuable.
I have had screaming (literally) arguments with a couple of vets about what to feed my animals. I don't consider a dried bag of baked to death dust/meal nuggets with an 'expiration' date years out, to be food. Mostly I just don't have that particular conversation with them any more. I don't consider doctors (human or animal) to be all knowing, or infallible. They ARE educated. Different thing. And some of them are very experienced. But some times we don't know what we don't know. My husband has terrible reactions to insect bites, especially spiders (not anaphylaxis), with huge swelling, redness, itching and oozing. All the ointments and remedies given by modern medicine don't really help. I use a poultice of echinacea angustifolia (the kind matters) and within 8 -12 hours the swelling and itch is reduced by at least half, often more. A long standing herbal remedy used for centuries, including for snake bite (I'm not advocating it's use for that), Dr's look at me like I'm nuts, and shrug me off. I figure if something is not going to do any harm, then why not try? It might work, who knows?
Conflicting advice is common, particularly with chickens (birds in general). I would say, weigh all you have heard and experienced, and do/follow that which makes the most sense to you and that you are most comfortable with. I know I tried it the first time out of complete desperation, and my bird recovered from what I was sure was going to be the end of him. I've used it numerous times since.
No hard feelings on my part, whatever you decide to do. It's your bird and your choice. I just share to try to give options to others in the same situation I was.
Hopefully the doxy helps, and the chlorhexidine may as well, that should not cause any problems. I use that all the time as well.