I think the problem with what we generically call “cold cuts” is that the majority of what people buy in stores and feed to their kids is usually mass-produced chemically-processed fairly disgusting stuff, and in general this is why it’s considered that things like this are “unhealthy,” which is probably accurate, certainly if consumed on a regular basis.
I now stay away from any of the big brands of foods like that. Similar with packaged sliced turkey.
On the other hand, as you get to better quality salame, and up to the fancy “artisan charcuterie” which is an expensive word for “baloney,” then it’s a much different story. But those are usually eaten in small quantities. They will still be high in fat and salt, that is the characteristic of how meat was preserved. But it’s a big difference in the meat (if it actually IS meat in the case of the factory-mass-produced stuff) quality, the spices, the natural processing as opposed to tons of chemical additives. That’s very different.