I'm not sure I believe that Valve ran out of ideas for HL3. That's clearly the image they want to project, and maybe even what they tell themselves, but judging from the ideas they did have for Episode 3 they showcased in that documentary, there was more than enough to justify releasing a game. Certainly there was as much or more new stuff than there was for either EP1 or 2. I think it's much more likely they simply decided their other projects at the time--CS:GO, DOTA 2, even TF2--had way more moneymaking potential. And I mean, they were right! They made a ton of money off of lootboxes and cosmetics for their multiplayer titles. I don't think Steam had totally taken over the market yet, so they were hedging their bets on multiplayer microtransactions.
I dunno. The whole "it needs to be new" philosophy they constantly espouse to hasn't really been true at least as far back as Portal 2. Even Alyx wasn't particularly revolutionary as far as VR titles go. Maybe doing that type of design was new to Valve, but the only standout features that distinguishes Alyx from other games are the graphics and the (genuinely very good) grabbity glove object pickup system. Pretty much everything else is several steps behind other VR shooter games in the name of Accessibility™, from movement to weapon selection to the painfully dumb AI.
They didn't run out of ideas. The movement FPS genre is alive and well for a reason, even today: there's lots to be done. They just lost interest in it themselves, and I believe the reason for that is primarily monetary.