Why wouldn't people have their language set correctly? Usually your browser language defaults to your system language, and presumably when you bought your computer, you selected your preferred language during the initial setup. If you had your browser set incorrectly, you would probably have dealt with that problem immediately when you saw all the menus and such in an unfamiliar language.

Perhaps some multilingual users might have one of their secondary language(s) set instead of their primary/preferred one, but at least it'll be a language they speak.

More importantly, even if the user has their browser screwed up, it's something that can be easily fixed on their end. But on sites that set language based on location, there isn't such an easy fix available; short of relocating or using a VPN, people in OP's situation are kinda screwed.

I don't run a German website, so I can't give you exact numbers, but in my experience, software can often default to something like 'en-US' in a variety of cases where you might not expect it to.

This is especially common in poorly localized tools. For example, a poorly implemented browser component inside some other tool or phone app might not properly set this value, and instead default to en-US.

Switching to the proposed method might fix the author's problem, but create a bunch of problems for other users in other scenarios.

Why wouldn’t Germans have their “browser languages configured correctly?”

German is well supported by software. If Germans want German content, they’ll have their OS set to use German.

Filipinos on the other hand would be a better example: Their software is likely to be in English but surely they prefer reading Tagalog or Cebuano.

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As a traveler, I’m thoroughly annoyed by being shown websites in the local language, but that would be perfectly fine if it was easy for me to change the language.

Sadly though changing the language often means having to learn what “Settings, Language, <language name>” looks like in the current country.

I don't run a German website, so I can't give you exact numbers, but in my experience, software can often default to something like 'en-US' in a variety of cases where you might not expect it to. This is especially common in poorly localized tools. For example, a poorly implemented browser component inside some other tool or phone app might not properly set this value, and instead default to en-US.

Switching to the proposed method might fix the author's problem, but create a bunch of problems for other users in other scenarios.

Not sure about German-speaking countries, but in Francophone countries, everything is in French. Even if the default is English, the user would insist on switching to the French version.