The internet already has a very simple interoperable protocol, HTTP. There is nothing to bolt on really since the pipe is just a channel for text and sockets on port 80 can just as easily act as those channel.
The thing about the pipe isn't, as I see it, a protocol issue, but a UI issue: that is, a simple method of telling your shell (browser, for an OS) to compose tools rather than requiring you to interact with each of them interactively.
To be fair, I don't think we have a good way to do that with graphical OS shells even on Unix, just CLIs, so its probably not surprising that we don't have it in web browsers.
HTTP is asymmetric (the two sides are not interchangeable), but the information flow is bidirectional. I don't see how that it prevents something like Unix piping from being implemented between web services using it. Seems to be mostly a UX design issue.
To be fair, I don't think we have a good way to do that with graphical OS shells even on Unix, just CLIs, so its probably not surprising that we don't have it in web browsers.