What motivated you to seek to change your mind?
This issue is one of those for which I believe there is no universal agreement.
So, it comes down to who you "want" to believe or what your current cleaning process has revealed relative to being adequate to achieve your performance goals. Also, you may want to do your own testing to satisfy your question.
I've always used a bronze brush for over 50 years now. Does it harm the barrel? I don't know but I don't think so IF you observe some basic precautions. Regardless, to me it's just logical that the mechanical action of the bronze brush does a better job removing carbon than not using one. However, some of these newer carbon removers, such as Bore Tech C4 does an amazing job removing carbon even with a nylon brush. Nevertheless, I still opt for the bronze brush since the limited tests I've conducted reveals that the bronze brush does a better job.
There are a few things you should do to minimize the potential for damage in cleaning a rifle bore.
1. Use a quality rod that rotates when pushing the rod through the bore. Wipe it clean after each pass to remove any debris.
2. Use a quality rod guide of the proper size.
3. Secure the rifle so it doesn't move while pushing a rod through it. I think this is overlooked. In my experience, nothing beats clamping the barrel into a bench vice with wooden protective pads. I've seen shooters clean rifles at the range and cringe watching them trying to keep the rifle steady while aggressively pushing a rod through the bore. Even with "cradles", I've seen the rifle become unsteady as the rod is pushed through the bore. With a barrel clamped in a bench vice, you can control the rod feed and develop a smooth uniform motion.
4. If you do use a bronze brush, use one with a brass core, looped ends, the proper size, and make sure that it is straight. For smaller calibers, like the 223, make sure that the crimp on the core is not belled at the end that will catch in the throat. Yes, I've seen this latter condition on some lots of brushes. NEVER reverse the brush while in the bore or using a 'sawing" action with the brush. Yes, I've seen guys do this at the range.
5. Removing the brush after passing it through the bore is perhaps an extra precaution if you're worried about crown damage. However, if you do reverse it after exiting the muzzle, go slowly to allow the brush to align with the bore. Don't ram it against the crown - go slowly. If the rifle is held securely in a bench vice, this is much easier to accomplish. I opt for the latter approach.
If you follow these simple precautions, in my experience, you will not damage the bore or crown using a bronze brush. But ultimately, you have to think this through and make your own decision because this is one of those issues for which there is no absolute, beyond a shadow of doubt, correct answer.