Binary is a number encoding scheme. You wouldn't be talking about binary if there were 3 possible digits. You'd be talking about trinary, or something like that. Computers used to use valves that would store values. Each valve would have a state depending on how much charge it contained. The problem with that was the valves lost charge and the values they were storing. People tried to think of ways to *recharge* the valves reliably for a while... but ultimately, this is why they started to use binary; If there's a charge it's a 1, otherwise it's a 0. It's more reliable.
Valves generate more noise and heat. They are **a lot** more expensive than transistors, but they're still used in audio. You're talking $5000 for a decent valve amplifier, where a $500 solid state amplifier might produce comparable sound. On the up-side, they do emit a very pretty light :)
In short, it's been done and I doubt we'll go back there. Valves may or may not work for audio, but they certainly do not work for computers.
![Valve audio amplifier :D]