1. Valve outgrew their gamedev ambitions, with their publishing arm. From millions to billions in profits, let alone gross revenue.
2. A physics based FPS with adequate action, level/game design and stellar writing needs a AAA team, which breeds innovation. They (most of the team) have left Valve. You can't just have a few puzzles with wooden boxes to get out of a room or use the gravity gun to move objects and call it Half-Life 3 (or EP 3) in 2023. The consumer is far more aware and played many of this ilk, many of HL's clones, even.
3. The hype for this game via memes, is far bigger than what it was in 2004/05, so big that no matter what they do, it can't satisfy the fans and critics. Alyx got lauded because VR is completely new platform.
4. Valve usually releases a slew of their IP's sequels with the launch of their new engine, and even when a distantly possible Source successor is out to the public, I don't think HL3 will, for the reasons listed above, just L4D and the next CS, maybe DoTA III?
5. Outsourcing will not work because how coveted of a flagship IP Half-Life is (I know CSGO and DoTA II, but what I mean is HL's legacy as the face of Valve). You don't trust your flagship IP, with any 3rd party team.
The closest we'll get to a possible/potential Half-Life 3 is either in VR or Gabe's vision of BCI - Brain Computer Interfaces - when they go mainstream. We're looking not just years, but decades...