Absolutely agree with #1. I've had a similar experience - I run a business with Stripe, also in Australia.
We charge in USD because we serve primarily US customers.
I pay for the business expenses in USD.
I've opened a US/USD bank account with Transferwise.
But I can't use it with Stripe [1]. Their only choice is to have them convert our USD earnings to AUD and pay out to an AUD bank account.
So when I pay those business expenses, I'm either:
a) paying on an Australian debit or credit card, which charge us another 3% for every international transaction (3% seems to be the standard rate across all of our banks here), or
b) carefully managing our cash flow to transfer AUD to our Transferwise account, use TW to exchange to USD, and then pay with our TW card.
We did (a) for a while, now trying (b), but I'd love to see (c): Stripe pays our USD earnings to our USD bank account.
[1] Funnily/strangely enough, I can actually ADD the USD bank account to our Stripe account. It just sits there, lonely, with a 0.00 USD balance. It took reading through the docs to realise that USD payouts are not supported for Australian Stripe accounts.