Technically speaking you are completely right. But we are humans and we, mainly, respond visually. Despite all the technical reasons, people will immediately locate the flag and switch. I did some bilingual sites, and some visitors, that knew the owners of the sites, suggested them about “improvements” of the websites but never commented about the flags.
I spent some time to find that you had the languages below, in the footer, and that is because I wanted to help and give suggestions. Visitors do not pay much attention to footers, they look for content of their interest, and where to find it (menus on top horizontal or left vertical, and the center area for content) A first-time visitor does not have much patience.
You can also use the language switch with the full language name and omit the flags and you save space in the header, especially if you have more than 2 languages. With the selector arrow it might catch the attention, but nothing like the flags for fast identification.
That is my humble opinion, aside from the standards.
If you prefer your languages text buttons in the footer like it is now, you have plenty of space below, so the switcher is not necessary.