In theory, we could either have one of us run a mining node for long enough to confirm the transaction or we could find a third-party miner to do it for us on whatever terms we could negotiate directly with them.

In practice, running a mining node without specialized equipment is prohibitively expensive so we're stuck finding a third party. Most of those third parties are looking to do a volume business and aren't interested in one-off small dollar transactions, so it's centralized exchanges or nothing.