> In the vast amount of cases there is never any (clear or otherwise) option to set the language of the site.
Unless manually disabled for privacy reasons (in which case... well yeah) your browser sends a weighted list of your language preferences with the HTTP request, the option on the site should only be an override.
> This has held true for Google as well as small mom and pops web shops.
Google follows the above language list unless your account or temporary session settings override it. Mom and pop probably don't know how to support more than one language let alone how to implement it well.
No, Google has per-country versions… which in turn support different languages. My preferred language is always English but Google normally redirects me to “Google Argentina” (.com.ar, in Spanish by default) from the .com based on my IP and I have to fight it to switch back to English. In some platforms / scenarios this means clicking on a “use google.com” link (or setting it in my Google settings), and in others I never managed to fix it. Google is a very frustrating case because it forces a redirect trying to be “smart” and there’s no way (I know of) to explicitly indicate through the URL that you want the default and not the regional variation.
Having multiple TLDs is not mutually exclusive with putting the browser language list first. Not every browser has always supported the language list (certainly not when the google.tld names were originally registered) and the TLD can serve to do more than change the default language.
> which in turn support different languages.
They'll default to a different language for the region in absence of any other setting (language list, account preference, browser cookies) but it's not the function of the TLD to override this when the information is present.
> My preferred language is always English but Google normally redirects me to “Google Argentina” (.com.ar, in Spanish by default) from the .com based on my IP and I have to fight it to switch back to English.
Redirection to a different TLD is based off geo-ip not your language setting and done for more reasons than just to serve you a specific language in absence of other language info. You're really fighting Google thinking you (or possibly your account) is coming from Argentina and your browser possibly not sending a language list (or a fake one). I had to correct something similar once where the IP block I had been coming out of had previously been in use somewhere in Asia, I just gave updated info to this form https://support.google.com/websearch/workflow/9308722?hl=en and it was updated and stopped redirecting me. Of course if you actually are coming from Argentina then they won't update it.
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Rather than a bunch of talk though here is an actual demo of what I get browsing to google.com.ar using English in the browser UI but with with German set as my preferred language in the language list: https://i.imgur.com/N3XOSvg.png clearly .com.ar didn't default to serving the page in German on its own nor was there any history in the browser so the language list the browser sends is preferred over the TLD you load. I'd double check you don't have a privacy setting or extension stripping this info.
Unless manually disabled for privacy reasons (in which case... well yeah) your browser sends a weighted list of your language preferences with the HTTP request, the option on the site should only be an override.
> This has held true for Google as well as small mom and pops web shops.
Google follows the above language list unless your account or temporary session settings override it. Mom and pop probably don't know how to support more than one language let alone how to implement it well.