>The DB AG has been specifically founded to be "market-oriented" and profit-making, so yes, it is true.

Again, if the shareholders decide this is the reason: yes.

But shareholders can just as easily set other targets or incentives.

>I guess it is also harder to market "let's subsidize this private company with tax payer money so they can continue to offer mediocre service" to voters,

The government owns DB AG, it is not a private company. It is a public company.