There is an absolutely beautiful rendering of the Mona Lisa encoded at some point in the digits of pi. If you know the position, it's really easy to plot the image.
>What benefit is there to keep this antiquated method around, aside from just as an historical reference?
Analogue clocks are, by design, also visual progress bars. Digital clocks just give you the time. There's a little video talking about this by Technology Connections: https://www.youtube.com/watch?v=NeopkvAP-ag
We assume an infinity of wave-functions correspond to a single physical process without difficulty.