I agree with RC20: the embedding thing is a little funny. If the softness of aluminum and brass let them embed, how much more easily would the much softer plastic coating on Dewey and other coated rods become flexible sandpaper? How about the soft coating on an Otis pull-through or the woven body of a Bore Snake? Yes, I would avoid laying any of those on a sandy surface, but to pick up enough grit to really wear a bore out if you push them straight through is difficult to imagine.
Rod wear, however, is a real thing that I've seen. I bought a couple of Columbian surplus '98 Mausers from Springfield Sporters back in the 80's. Four of us actually stopped at their shop while driving through Pennsylvania. That let us inspect the re-finished Mausers in substantial numbers to pick out the ones we liked best. Many had barrels whose crowns were funneled open in a rifling-free oval with a strong wear bias to the bottom side of the muzzle. It was clear that generations of Columbian soldiers had used the rusty steel cleaning rods kept in the underside of the stocks of these guns to run bore brushes back and forth while standing the gun up on its butt plate and with gravity pulling the top side of the rifle toward falling over. The muzzle turns out to make a poor journal bearing for rusty cleaning rods. Anyone cleaning from the muzze really should use a guide of some kind.
I've worn the coating off most of the Dewey rods I have and don't care for the non-standard 10-32 male thread and put 8-32 femal threaded adapters on mine long ago. As a result, I find I use an old straight stainless rod I bought under the Rig brand name decades ago. It is easy to wipe off, it has no coating to wear, it doesn't rust, it is smooth and won't abrade anything appreciably. I do, however, use bore guides and have ever since seeing the Columbian Mauser barrel collection. Especially with .22 Rimfire barrels, which I find are often quite soft. I keep a some 5/8" and 3/4" Delryn stock and turn my own guides out of that when I don't have one that fits quite right.
I also avoid using cleaning rods excessively at all. With Boretech Eliminator I find that if I keep a small pump sprayer of it in my range kit, when I finish a range session I just pump enough in the breech to see it running down the bore, plug the muzzle and breech and case the gun to go home. By the time I get home a single patch often cleans it pretty completely. I do use the Boretech Proof Positive jags as I do get some light blue off my brass jags with this product. It attacks copper very, very quickly and, unlike ammonia, it isn't easily worn out by the attack. It is able to sequester the copper in a chelated form that frees the attacking part of the chemistry up to go after more copper. So it can eat a lot of copper. I run a wet patch at home followed by a dry patch 20 minutes later, just to make sure there's nothing left, but with all but rapid fouling bores, three patches are generally all I need. I retired my bore brushes completely. They just aren't needed with this vastly superior modern chemistry, especially if you've applied it while the barrel is still warm and the carbon hasn't yet hardened. Read
this article on Slip2000's site.
The Otis pull-through is particularly useful with semi-auto and pump actions that don't give you a straight cleaning rod shot into the breech (Garand, M14/M1A, BAR, Rem 760/7600 and 740/742/7400 etc.). Same with a lever action if you want to clean it without disassembly. I've also made muzzle bore guides for these kinds of guns, but prefer not to push solvent and crud toward the breech where it can fall into the action and bedding if I'm not careful.