You should have doubts because every website you look at is on a device that most likely has tons of parts written in C.
Pretty much any piece of hardware you run your browser on, irrespective of whether you're looking at a website that has javascript code or not, has some C code running to support your javascript VM, browser, and operating system.
Whether you're on a computer, cell phone, gaming console, IoT device, you name it... you're most likely executing some C code quite frequently. And that's whether you're using a browser or not.
C is still the go-to language (no pun intended) for pretty much all drivers (with certain parts in assembly as needed) of any piece of hardware.