Not quite Half-Life 3, but close enough - Pancake FPS Starter Kit helps you play Half Life: Alyx without a VR headset
Pancake VR Starter Kit, a mod for Valve's Half-Life: Alyx makes it possible to play through the latest game in the Half-Life series without needing a VR headset like the Oculus Rift, HTC Vive, or Valve's own Index.
The Pancake VR Starter Kit adds in weapons from Half-Life 2 as well as allowing modders to implement custom weapon scripts. As the gameplay video indicates, it also apparently changes the view model to get rid of the distracting VR hands.
It's interesting to note that Pancake VR wasn't actually created with the stated aim of making Half-Life: Alyx playable on regular "pancake" displays. In fact, the creator even has a disclaimer up on the mod's Github page saying "Please don't use this to play Half-Life: Alyx and then complain about the game being bad!!!"
Nevertheless, the static viewmodel and the addition of Half-Life 2 weapons means that, unlike with earlier VR mods, Half-Life: Alyx now plays more or less like a standard first-person shooter.
If you wanted to play the game but didn't want to dish out an eye-popping US$999 for the Valve Index, Half-Life: Alyx with the Pancake VR Starter Kit might be the best way to experience Half-Life until/if Half-Life 3 comes around.