If we’re both willing to pay that in a free market economy, then we both leave the deal happy.

Things are worth what people are willing to pay for them. And that can change over time.

Sentiment matters more than fundamental value in the short term.

Long term, on a timescale of a decade or more, it’s different.

Both parties would need the $1B prior to the transaction for it to even potentially be meaningful, and still they just traded a cat for a dog and only paid each other on paper.

That ultimately wouldn't be a big deal if the paper valuation from the trade didn't matter. As it stands, though, both parties could log it as both revenue and expenses, and being public companies their valuation, and debt they can borrow against it, is based in part on revenue numbers. If the number was meaningless who cares, but the numbers aren't meaningless and at such a scale they can impact the entire economy.

> If we’re both willing to pay that in a free market economy

The thing is: you've paid nothing - all you did was trade pets and played an accounting trick to make them seem more valuable than they are.

Is that not fraud?

Yes, it is fraud round tripping is fraud, whether the government is willing to prosecute it or not.