Neither Wifi nor Bluetooth are a 1:1 replacement for wireless USB, in that neither allow you to use a standard USB device without a wired path between the device and host.
In theory, Bluetooth ought to be the replacement for most use cases, and would simply require replacing your USB devices with Bluetooth devices. In practice, Bluetooth is still kind of terrible, so I'm tempted to say any alternative timeline where something else won the personal area network war would probably be better.
We still kind of do wireless USB, in that the standard for wireless mouse and keyboards is still not Bluetooth, but a dedicated USB dongle that ships with the device. Such options are available for wireless headsets as well, although Bluetooth seems to winning in that niche.
It used to be the case that BT was terrible, but in the last few years I have increasingly stable device connections. Could it be they simply ironed out the bugs over the years, the standard matured, and also the manufacturers are more compliant? It just works for me, no horror stories. And BT LE is indeed low energy.
Btw, do you have any other suspected reason (politics aside) that wireless USB did not catch on?
The real change is that BT LE isn't just about low energy. That might have actually been the original intention, but in practice it is so good beyond that core area of competence that it has also displaced classic Bluetooth in fields like audio streaming, connections beyond strictly PAN distance and so on. And it will only get better as more remnants of Old Bluetooth are disappearing from devices, that have been retained for backwards compatibility.
In theory, Bluetooth ought to be the replacement for most use cases, and would simply require replacing your USB devices with Bluetooth devices. In practice, Bluetooth is still kind of terrible, so I'm tempted to say any alternative timeline where something else won the personal area network war would probably be better.
We still kind of do wireless USB, in that the standard for wireless mouse and keyboards is still not Bluetooth, but a dedicated USB dongle that ships with the device. Such options are available for wireless headsets as well, although Bluetooth seems to winning in that niche.