What kind of washer do you use. That has a big impact on general wear and tear of cloth.

I don't know. I live in an apartment building and use the general laundry room.

Sounds more like lint coming off, not pilling. I always put new bath towels in the dryer, with no heat, for a few cycles to remove most of the lint before the initial wash. Vinegar does nothing, although whoever told you it would control lint probably meant well. Vinegar used to be popular for setting dyes, but it is rather useless.

Thank you. I will try to put them in dryer no heat. Hope that works.

If linting is the source then washing will continue to generate it until the fabric "wears-in" and linting lessens. Washing always causes damage to fabric, whether it be minimal/imperceptible or clearly noticeable such as shrinking.

I think the question of what type of washer was in general terms ... agitator toploader, HE/impeller toploader, or frontloader.

He frontloader.

Lint can come from the washer agitation breaking the cloth fibers. The dryer tumbling then allows these broken fibers to break away from the towels as lint. High end, home machines minimize lint

Commercial laundry is made for durability, not gentle cleaning. Big holes in the washer drum allow the towels to be pushed through during the spin cycle causing small thread breakage. This then comes off as lint.

Probably not much you can do. They will eventually lose most of the loose weave during the "wear in" phase.