You could, but it is a bit pointless. The idea is that mathematically a superposition of analog waves looks the same as the superposition of quantum states, so you can get exactly the same behaviour using the natural laws of physics. A digital system that modelled the waves would require an absurd amount of resolution since the interference effects need to be modelled accurately. In essence you are throwing away most of your information capacity by switching to digital on/off signals from superimposed waves even though you are using the same wires. The reason quantum computing is interesting in the first place is to use all that wasted information to produce a Massive gain in computing power in a much smaller system.

Probably because an analog signal will provide a continuous high-resolution sweep of values, without any aliasing.

You can resolve continuous ranges of values with very high precision, albeit at the expense of exacting and repeatable accuracy.

Digital circuits work fine for simulating, and emulating, quantum computers. They probably chose analog circuits because that's what they like to work with, or because the more-direct encoding allows for efficiencies.

Probably has something to do with the determinism of digital systems.