Why do watchmakers insist on polishing the watch case?

yes, yesterday
And, yes, today, except for us, the very Minuscule Minority

I think back in the day, there was a sense that the job wasn't done unless you pressed the case against a polishing wheel for a few minutes to make it look shiny. It's an outdated idea that many have trouble backing away from who are in the profession. My personal policy is that refinishing must be requested, and it is not automatic. I separate the charge for it so that people who don't want it, aren't paying for it.

I often see on watch forums people say that you need to find an "old time" watchmaker for best results. Well, sometimes that comes with baggage like this and outdated techniques that aren't up to modern standards...

Not really just "us" in the collector world. I do a lot of work for collectors, but also for non-collectors. Most non-collectors are, in my experience, not looking to have a watch refinished either, and some collectors do request it.

Not wanting your watch refinished isn't as strange as some here may believe.

The main watchmaker I use has a strict “no cosmetic work unless specified” I have to Actually write it down. Even a crystal polish. He doesn’t mind doing it a crystal polish used to be automatic (depending on the crystal) but he actually has people get upset about polishing a crystal enough times where he leaves it as is unless you ask for it. I do find that a bit odd but he did 20 years with swatch and I think 15 now independent I guess he has earned the right to be particular. So I just right it down on the slip when I bring him a watch and it’s taken care of.
He did some really nice gold work on my last gold watch. I was planning on keeping it as I had 6-7 vintage gold pieces some pretty unusual though not of great value but I had someone who has been dying to buy it and he went through some tough family stuff recently so I relented and sold it to him. It will help me get a newer seamaster which will make me happy and he’s happy because he’s crazy about gold watches so it worked out all around.
If a watchmaker is running a business and he just wants me to write down on his invoice thing I want him to polish the crystal and do gold work on the case I have no qualms it’s his business, he doesn’t charge for polishing a crystal. He will of course charge for gold work but anyway I like the “no cosmetic work unless specified” the crystal may be a bit overboard but so what I write it on a piece of paper and it’s taken care of.

About ten years ago I had a 1951 day/date/month/moon watch overhauled by a very well known national shop in PA. I told them not to polish the case and they didn't, but when I opened it up just to check out the work I found the watch repairer had scratch marked the previously unmarked, pearl sheened case like repairers did in the old days. I called the owner of the shop to tell him that was unacceptable these days. He apologized and said the repairer was 'old school' and that was just the way he operated and they have told him not to do that, but he continued to do so. So, yes, you can't blindly let oldie guys do their thing, some past practices just aren't acceptable any longer.