But if they subsidize the hardware, non game users will purchase the hardware and use it for non game use-cases, where valve cannot recoupe the costs.

A interesting scenario would be to sell the hardware at cost, but include a 30% off ticket to the steam store (up to a few hundred dollars, in savings).

Instead they made the right choice and subsidise the software. Valve has been sending patches for Linux for over the last 10 years as well as giving SteamOS out for free for other hardware now.

If you don't want to play games, why would you buy a steam machine? Even with a subsidized price, you could get a mini PC with no GPU for half that or less.