The reason no one is making HL3 is because no one wants to, at least not long term.
Idk if you know much about how Valve is structured as a game studio, but it’s a bit atypical. It’s not like Gabe Newell comes in and says “today everybody starts working on HL3”, projects get greenlit and then whichever employees want to work on them are free to do so, and if they decide they’re uninterested, for whatever reason, they can leave the project.
What this means, is that if a project starts to pick up steam (no pun intended) within the company, more and more people join in, and this creates a passionate team. Various Half-Life projects since Ep2 have been started, none were finished (until Alyx), not because they were decisively axed for more corporate reasons like many other games, but because for one reason or another, the devs became uninterested or burned out, and went to work on other things they actually wanted to work on.
I think at this point, the only way we’ll ever see HL3 is if a team comes up with something completely groundbreaking and is absolutely dedicated to getting it done. Apparently, there just hasn’t been that winning combo yet. I can’t blame them, because if they half assed any aspect of it, they’d never hear the end of it.