First a foremost, I benefit in no way from what people use to polish their pipe bands with. I do not even make money off of the jeweler's cloths. However, the jeweler's cloths do not use a low PH compound to remove the tarnish. They actually polish off the tarnish, leaving a polished surface. Ash may be better, if it doesn't actually remove the silver in the alloy, given that it is not actually abrading the surface also. I can't say what ash would be better; however, just feeling the ash in your fingers doesn't tell you whether it has no grit in there, because our senses at that microbic level just can't detect it.
However, one of the other benefits of a jeweler's cloth is that it also polishes the stem. Also, the outside of the cloth (depending on what brand it is) leaves either a microcrystalline wax on the surface or a patina inhibitor. The patina inhibitor has an unusual smell to it, which is how you'd tell the difference. But, both will prevent future tarnish, but also oils from your skin in holding the band can do this as well.
Otherwise, I am rather neutral on what someone uses. However, if someone uses a paste or solvent based cleaner, like those sold in big box stores, they are removing layers of silver that could lead to a thinning of the band, that could jeopardize the integrity.
That all said, despite popular notions, I did not invent gold... I merely perfect it's use, ha ha.