C is used when extra high performance required for some heavy loaded modules which requires calculations. Many big companies, including, Facebook, later rewritten some parts on C.
For the most companies around the world there is no need in such performance and complexity at the beginning.
Web is very flexible, requires usage of many 3rd party APIs and JSON and dynamic languages are better suitable for that job, while in C you need to write and think about very small details and later controlling all that codebase is what you will fight. C requires also much more knowledge then PHP or JavaScript, thus much harder and more expensive will be to hire an engineer. One of the core functions in the modern web - dealing with JSON, which in C is a real pain.
Answering your question from the point of view you are asking it - No, nobody in his clear mind will not be writing web app in C at the beginning. It will be too long and too expensive, while with modern CPUs, GPUs and cheap VPNs, cloud there wouldn't be any real difference for business.
However, web evolves and WASM (WebAssembly) is coming. That means C will be used more in Web in the future, but, again - to bring some modules with highest performance to the market. WASM are like JavaScript modules written in a way similar to PHP extensions - you import compiled WASM into JS itself to use it functions. Most of the general code will still be written on JS/PHP/Java/whatever.