Sure, argv[0] is a just string, that the caller can set when they call execve(). That doesn't have mean that it doesn't have meaning. You are correct, there is no way to know how your executable was passed as the first argument to execve(). But, argv[0] is specified to mean roughly "welcome to the world, you are argv[0]", and to tell the program what it is. Sure, you could lie to the program, and tell it that it's something it's not by passing a different string to execve(), you can even do this from a Bash script with `exec -a`.
I stand by my original statement: If you want to tell the user how to invoke the program again, argv[0] is the right thing. I didn't say that running argv[0] will necessarily actually invoke the program again, I said that it's the right thing to tell the user. If the caller set argv[0] to something else, it's because they wanted your program to believe that is its identity, so that's what it should represent its identity as to the user.
Do note that was my complaint with $0, that when using $PATH it was set to that full gross path.
If /bin/foo is actually /nix/store/3508wrguwrgu3h5y9354rhfgw056y-foo-5.0/bin/foo, then when you run "foo", 0="/nix/store/3508wrguwrgu3h5y9354rhfgw056y-foo-5.0/bin/foo" and BASH_ARGV0="foo".
I stand by my original statement: If you want to tell the user how to invoke the program again, argv[0] is the right thing. I didn't say that running argv[0] will necessarily actually invoke the program again, I said that it's the right thing to tell the user. If the caller set argv[0] to something else, it's because they wanted your program to believe that is its identity, so that's what it should represent its identity as to the user.