There is nothing wrong with that logic but there is something wrong with yours. Valve has to run steam, which includes indefinitely hosting a growing number of games. The bandwidth, hosting, and technical competence does not come free, thus it's impossible to offer the service for free and why should they?
Originally Posted by DanLamb
They may have a solid position on the market but steam is not a natural monopoly other than the desire to have all your games under one service. Anyone can self publish a game and yet valves customers, which includes both publishers and gamers, find it beneficial to utilise the steam platform. That's the market working.