But they do run it to maximize profit. There's just allowed to do it creatively instead of obsessing over short term gains.

I mean the company essentially gave up on AAA games for well over a decade because they were making more money from steam, and Gabe famously only approves projects that have a plan to turn a profit or expand Valve's market.

They didn't spread into Linux out of sheer principle. It gives them more control and influence over the market to separate themselves from Windows. And they've done tons of shady stuff with steam like refusing to give refunds until they were sued by state governments.