That is not what's happening. TCP is entirely in the kernel. You are confusing Winsock with TCP.
Even then, Winsock has it's own driver (AFD.sys, which definitely does not stand for Another Fucking Driver) as well.
Most of the user-mode Winsock (ws2_32.dll, mswsock.dll, ws2tcpip.dll) implement the Winsock 2.0 spec-related bookkeeping, but Winsock calls essentially boil down to Ioctl()s to AFD.sys in the common case.
The thing to realize is that Winsock 2.0 was spec-ed at a time when Windows NT (and 95) allowed vendors to install things called "layered service providers", which were providers that hooked into Winsock and allowed you to intercept/redirect/filter various Winsock calls. Lots of internet filters worked in this way in the early days.
Now, given that these 3rd party providers were free to implement their protocol in user space completely, the socket handle you got was not guaranteed to be a kernel handle (Called an IFS handle all over Winsock documentation, for Installable FileSystem handle. )
Thus, WSADuplicateSocket() was a way to allow these providers to re-create a socket based on whatever provider-specific information was passed in through IPC.
Going back to your original claim, you can actually take a native AFD socket handle to a TCP connection and duplicate it (with DuplicateHandle) into another processes. It will also probably work just fine, but no one at Microsoft is going to officially support this usage, for the above-mentioned compatibility reasons, even though Winsock layered providers are officially deprecated now.
Edit: clarified what I meant by duplicate in last paragraph.
And I guess one could still implement an LSP in the user mode while supporting DuplicateHandle directly, without all the WSADuplicateSocket stuff, by having a service with all the custom logic, and returning pipes into this service as socket handles. That's basically what a microkernel would do as well, right?
Haven't thought about microkernels in a couple of decades :), but yes, I can see how what you are saying could work since the handle will technically be a duplicatable kernel handle. It might be better for the service (or subsystem in NT microkernel terminology) to have a driver so that the client can reference it with a proper, dedicated handle, but that's a bit beyond my wheelhouse as to which approach is better.
Edit: Completely forgot about ws2ifsl.sys which is a driver that exists just to give Non-IFS providers a kernel handle with the WPUCreateSocketHandle() call !
Windows TCP sockets are definitely their own thing, which is pretty unfortunate, but Windows exposes a number of other kernel abstractions as handles - processes, mutexes, shared memory sections, events, timers, &c; “Wait for either this particular process to exit or this timer to expire” is trivial. At the time I worked on it, it was one of the features I really preferred about Windows over Unix.
And Win8 added nested jobs, so now you can basically have inescapable process groups with "if the leader process dies, terminate all its children and grandchildren" semantics. On Linux, I had to just give up and use Docker containers for this: some software simply insists on daemonizing itself too much, to the point that on receiving SIGTERM, it re-sends SIGTERM to everyone in its process group (including you, the unsuspecting parent. That was very "funny" to debug).
But of course, the downside of Windows is that the amount of legacy crap and weird quirks and incompatibilities is insane, even more than in x86. "The Windows low-level APIs wouldn't recognize "general" if it showed up in a uniform with stars on the shoulder." (c) njsmith
However, because in Windows TCP sockets are implemented in the user space, you can't quite use this routine to pass sockets: the part of its state in the user-space won't get duplicated (well, you can't send FILE* into another process in neither Linux nor Windows, right), so there is WSADuplicateSocket function which doesn't actually duplicates the socket, it gives you a struct full of its internal state which you have to send to another process somehow, and then the other process has to re-create the socket manually, by passing this struct into WSASocket call... and I've no idea how the inter-process sharing is then set up, but apparently it is set up, so those two sockets would actually have synchronized state from then on.