Neither does money "travel between the US and Australia" for a regular old SWIFT and correspondent banking based international bank transfer. When you send money internationally, your bank also "taps into pools of local currency" of their various correspondent bank(s). All of this could also happen instantly if they wanted it to; SWIFT is a real-time messaging network.

Wise's innovation was to provide their service "over the top", i.e. unbundle wire transfers from your bank's default offering. This has driven down both speed and pricing, in the same way that dial-through (e.g. calling card based) long distance carriers created massive competition and drove prices down in long distance calling, while under the hood it was all still just regular phone calls.

When you send USD to an AUD account by any mechanism no money actually travels between the US and Australia. Usually USD is transferred from one US bank to another, and AUD is transferred from one Australian bank to another.