The signal reflections from the stub can propagate all the way back to the source. This means you’d have to use two transmitters to avoid interference from those reflections.

If there’s only one wire in the cable, and one trace leading up to the socket, would there still be a stub? Have the sockets pins both tied to the same trace, and have the plug terminals both tie to the same wire.

I'm not an expert; but having splits and merges in your traces and wires when you need to have matched signal path length seems like a terrible idea.

The four additional pins are a nontrivial problem. The Type-C connector is already annoyingly large as is. The stubs others have talked about are a major problem; they're really hard to avoid. In fact, they're so hard to deal with, that a lot of effort in routing goes to keeping things in the right order on the board.

By that I mean that when you leave, say, your upstream device and run the traces to downstream, you need to have them come out in the same order: if you start with _P on the left and _N on the right, you want to end that way. A swapover is annoying at USB 2 480Mbps speeds and utterly awful at 20Gbps. (There is also a >50% chance that you miswired the thing and are wiring _P to _N, which increases to >99% if the routing came out naturally neat, but that's just Murphy's Law in action.) It's so difficult and awful to deal with this stuff that USB 3 took a page from Gigabit Ethernet and usually features transceivers that just figure it out: they know you have eight wires in four pairs between eight pins and they can work with that.

Once you have that feature, and transceivers definitely do, there is no point whatsoever in trying to make superfluous changes at the connector bit.

The splits and merges would definitely affect signal integrity. Signal integrity is one of those fields that can feel like dark voodoo magic. I know people who are signal integrity experts by trade.

Would the splits and merges definitely make the signal integrity worse to the point that it wouldn't work? Maybe not. But if you're designing a high speed cutting edge standard, you probably don't want to make decisions that limit the best signal integrity an implementer could achieve. Signal integrity is all about balancing the bad SI decisions you have to make because of some product goal or whatever with tighter tolerances elsewhere. The more "clean" the standard is, the more tolerance it has for the implementers.