It's not "Web", it's "the Web".

The "the" is a signifier that it's the one and only, a singleton.

The original "World Wide" could be elided as it became clear which Web everyone was talking about.

But the "the" could never go away.

If there were a sub-island of the web, then even if you added a single interconnect to the rest of the web, it would join into the web.

With such an open, interconnected fabric, it's impossible to keep subcomponents apart.

It wants to be one.

If you're going to make a single, common, planetary-scale fabric of computing like the web, it's got to have "the" in the name.