Valve has no commercial interest in making Half-Life 3. It's not that the game wouldn't be profitable. It almost certainly would be - lots of people would buy it. But it would risk the wider strategy they've been pursuing for a decade now.
Valve's income these days isn't from making and selling games; it's from charging other people to sell games via Steam. Seriously - you buy a game on Steam and a big slug of the price you pay goes straight to Valve. Sure, they have hosting costs, but there is a lot of pure profit in there.
Ever since Steam started to be a big thing, Valve has focussed on more niche games rather than big-budget fpses. It does not want to be seen as threatening or a rival to its biggest business partners. EA have already taken their toys and gone home to Origin; Valve's dominance of the PC gaming market relies on keeping Activision, Ubisoft and others on board.
And a big part of that is not being seen as a competitor. If Activision wants to pay Valve a lot of money to plaster the Steam front-page with a huge Call of Duty advert, then that's good for Valve. But Activision might get nervous if they worried that the platform they were using was run by a company that was actively pushing a game in competition with theirs.
Over in console-land, Sony and Microsoft's first party exclusives are generally put out there to sell consoles (not always a profitable activity in itself). They build up the installed base to get the third parties interested. The only platform-owner to really emphasise first-party games development is Nintendo, who, surprise surprise, have terrible third-party relationships.
Far easier for Valve to allow other people to put the effort in to making money for them, rather than take the risk of investing in games development to make direct income from sales. Particularly now that Steam is so ubiquitous as a platform that it doesn't need first-party games to grow the installed base.