Hey Abishek, this is an interesting need that you bring up. There are a few different ways to approach this problem, but for sqwok.im I am working from an angle of first creating a public chat platform with a high-quality chat interface, that can at a later time be used as an embed etc.
My motivations for sqwok.im are somewhat diverse but center around a strong belief that we need more competition in the social arena, and the current incumbents don't provide a product that matches my vision for sqwok.
Sqwok is a simple, but high-powered public chat app. Anyone can create their own chat room and share it simply through a url.
The mechanism sqwok is built on also means it's primed for the use-case you mention which is allowing site-owners to add a chat interface for their own pages (c2c). Most chat widget companies are focused on b2c right now, and there is a thriving market for that. But as you identified, there is an opportunity to create a way for everyone on any webpage to chat with each other.
I have been working hard on sqwok.im and plan to deliver in this arena. Would love to chat more!
There are many problems to solve and it's not straight forward.