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There is no financial gain but you can't say there is no direct advantage while running your own node, cause you don't need to rely to 3rd party to validate your transaction. Also when you run your own node the privacy of the address and transaction history seems to be more valuable than few sats.
I don't understand something here. When I use an exchange, such as Coinbase, they do all the work. Or at least get it started. When I use a wallet, such as Trezor, the request is submitted to the Bitcoin network and some number of the Bitcoin nodes validate the transaction. In the response you wrote, I get the hint that I might need to do something more to validate the transaction. Please explain a bit more.