Valve is lucky it came up with Stream before any real alternatives arose.
Extremely lucky.
Yeah it was pretty lucky to make a cinematic FPS before that was really a thing, they were lucky to push mods into full fledged games, they were lucky to make the small portal puzzle game which drove a whole lot of other small puzzle games, they were lucky to release steam the biggest distribution platform in the world, they were lucky to make l4d one of the first online co-op games (using a complex learning AI for difficulty), they were lucky for doing the item economy, lucky for doing good VR research, lucky for doing the lighthouse system.
It is truly amazing just how lucky valve is, I'm thinking the all we want hour employees to be T-Shaped is just a facade that instead of a T what they really want is for the employees to be double L back to back to bring all that luck into the company.
I'll take 3 VR games over HL3 any day of the week. HL3 will never ever live up to expectations of it even releases.
More importantly the last thing this industry needs is more studios just doing sequels.
Of course they care. That's why Steam gets new features and Dota, TF, CS are still supported. As you said those are all bigger than HL now. It's their current customer base. Valve is serving them, wether you think adequately or not that's another thing, but they do.
Supporting their fanbase and deciding things based on what is going to please the biggest amount of their fanbase are not the same thing, I'm sure they care about their fanbase, but pleasing their existing fanbase certainly isn't what decides the next project they, since as I said they would still be doing half life if that was the case.
Valve is mostly about creating value to the consumer, which is not the same thing as their fanbase, not unless we assume that valve has a fanbase of over 100 million people.