Because, according to the new rule, it's only permitted in proper names

"Eva's Blumenladen" is the proper name of the shop, what is put on the sign above the door.

"Evas Brille" is just Eva's glasses.

Oh shoot, I read it as Eva's Glasses, the name of her eyewear shop.

That would be "Eva’s Brillenladen".

That’s not a given, the store could easily be called "Eva’s Brille", I’d say that’s even more likely than the archaic sounding Brillenladen.

... but even before the rule change, in virtue of being a proper name, if the proprietor calls it "Eva's Blumenladen", and it's marked as such, wasn't it proper usage to refer to it that way? If I call my English business, "Joes Cafe" (intentionally not using an apostrophe), wouldn't it be incorrect for people to refer to it in writing as "Joe's Cafe"?

Absolutely. You don’t need to come up with fake examples. Take a couple of high end British retail establishments: Harrods and Selfridges, founded by Messers Harrod and Selfridge, and neither styles itself with an apostrophe.

Define "proper usage". You can call it anything you want, but if you call it "Evas Blummenladen", people will wonder why you spelled "Blumen" wrong. Now sometimes people do that in names as a play on words etc., but here it just doesn't make sense.

In the same way, people will wonder why you spelled "Eva's" in "Eva's Blumenladen" wrong, if you spell it that way.

Yes, if enough people start doing a wrong thing, it'll eventually become "right", and I guess in 100 year's we can put apostrophy's where'ever we wa'nt, but currently it still looks odd, and like something that is foreign to German, and imported from English. Because unlike in English, in German this apostrophy doesn't stand for an omitted letter in the genitive singular ending.

CAESARS is correct because it’s a palace of Caesars, not of the Caesar. Something to think about while you’re stuck in Las Vegas traffic.

https://www.caesars.com/caesars-palace/things-to-do/nightlif...

The former are names of businesses, the latter is just referring to someone's personal item.

(This confused the heck out of me at first too.)

But I can style the name of my business however I want, "E'v'a's Blumenladen" is correct because I say so. I don't need anyones approval.

In Germany you need approval for business names.

Do you really? In other European countries you only need approval for your company name, but are free to use any business name(s) you prefer, as long as they're not trademarked.

Peter’s Taverne is the name of the tavern, Eva's Brille is just eva's glasses not a the name of her store.

So Evas Blumenladen is called Eva's Blumenladen is correct.