The UK also has favourable visa arrangements for Australians - certainly more so than the US, which seems hell bent on rejecting any desirable immigration.

That's not the case. It's not very easy for an Australian to get a UK Working Visa in their own field (as opposed to "working holiday" arrangements).

OTOH, the E3 US Visa is quite simple - it's generally considered to be the easiest US skilled worker visa to get.

As a Canadian working in the US I would love to have access to an E3. It's way better than our TN visa.

Roaming charges tend to be regulated in Europe so you will likely know what you will need to pay.