Should websites be able to dictate which programs can access them? In a way a website is just an API too.

They do. Many of them expect Chrome. While Safari and Firefox are now much better supported than years past due to most sites complying with web standards, I still see some annoying incompatibilities here and there with older finance websites. I didn’t like it, so I switched to a larger bank. Your argument would have more teeth if meta had a monopoly. It doesn’t