Why wouldn't they make a Half Life 3. It makes so much financial sense.
Also what every happened to Half Life 2 episode 3?
They started making DLC for Half Life 2 and release Episode 1 and 2 but 3 is still MIA.
It's similar to why square took so long to make a Final Fantasy 7 remake, because riding on the existence of an unsullied previous product, no matter how distant, is better than sullying it. Look at star wars, people still loved the OT when the prequels came out, now Star Wars interest is at an all time low. Valve are judged on their previous projects, and while HL3 doesn't exist their previous projects remain pretty stellar across the board. Making a large entry to the series just opens them up for criticism, criticism that can create upset in their core business, which is now selling other people's games. The risk of getting HL3 wrong could be company ending.