Can I route a differential pair as two separate, length-matched, single-ended traces with half the original impedance on each?
Can you? Yes. Should you? Probably not. The reason they are handled the way they are is that the tight coupling gives them Common Mode Rejection.
That’s essentially what you are always doing, but if you want to optimize them, then you route them as a “pair”(diff pair)
Yes, it is possible to route differential signals as two flight-time matched single-ended signals. After all, bringing such signals into test instruments like VNAs always work this way.
On a PCB there are several benefits of routing them as a differential pair:
(1) They are spaced closer together and so take less board space.
(2) Coupling between the signals is greater and as they are equal and opposite the result is the losses are reduced.
(3) as has already been stated, common mode rejection is improved because the proximity of the two to each other means the coupled in noise is more alike in each conductor and so cancels out better at the receiver.
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