Gary Illyes from Google said on LinkedIn that if you want to you can use a single robots.txt file for all your international sites. He added that he is not saying this is a good idea, but rather, technically, you can implement your robots.txt this way.
Gary wrote, “Technically you could have a single central robots.txt for all your international sites (de.example, ch.example, at.example, etc.) that’s hosted on your CDN (cdn.example/robots.txt).”
Although, Gary later added, “Not saying it’s a good idea, or bad for that matter, just that it’s possible.”
Now, Ohgm wrote about this several years ago over here if you want a more detailed technical walkthrough.
But this is just another SEO PSA from Gary.
Forum discussion at LinkedIn.