Company gets a cut of every game sold, gets exponentially more customers that use your infrastructure on a day to day basis, meanwhile the price of games stays the same for 20 years and game development cycles get longer while games and infrastructure gets more expensive to make.

I wonder how Valve hasn't gone bankrupt.

I don’t. Valve is in a super sweet spot in the market and their near-monopoly on PC game sales and lean business model gives them a lot of breathing room that Companies like Sony don’t have. Some benefits Valve has:

• They don’t need to worry about R&D of exclusive hardware often sold at a loss just to capture a user base. Valve has dipped its toes into hardware now, but even if its competitors eat some of its market share, those users will still buy games from Steam. On the other hand If people buy an Xbox instead of a PlayStation, Sony just loses out on the customers.
• Valve doesn’t have to operate a number of first and second party game studios to churn out increasingly more expensive games.
• Steam being a storefront on another company’s operating system means it can rely on external infrastructure to handle user services in many of its games.
• Valve is a privately owned company so they have a lot more wiggle room to tread water and “stay afloat” when necessary and aren’t being driven to an ever-increasing profitability targets year after year.

Valve literally can’t charge you for their user services because you’re not stuck on their hardware. The very moment they do, they’ll lose all the user goodwill that has made them the default in their space and everybody can just pack up and move to another storefront or even just pirate their games. Valve has to eat those costs at the expense of everything else.”, they have no choice.