It's just that you write it once and it can run anywhere without "installing" many dependencies other than a browser. No fugly GUIs, no inconsistencies, etc.
By web-based I didn't mean it to be on the Internet.
Absolutely — you just open a high port on localhost and open the URL in a browser. I've used this technique before on consulting projects with great success.
I've actually thought about making something like this.
My reasons: collaborative coding + debugging, and IDEs without needing an environment aside from your browser (coding + compiling + debugging code on the device it's made for).
...why would you want to do that for a C debugger?