Half-Life writer Mark Laidlaw said in an interview that he expected Valve's game to have a wider impact on the approach to building storytelling in first-person shooters.
Continuous storytelling without cutscenes never became the "standard" for the gaming industry. However, Mark did highlight a couple of examples of games in which the influence of Half-Life was sometimes visible:
I must confess, there turned out to be far fewer [of these games] than I expected. I suppose it's quite a risky business...such storytelling rules that we implemented should only be applied if you are sure that something worthwhile will come of it. Nevertheless, I have seen many examples where the influence of Half-Life is applied in fragments — Medal of Honor, for example, and Call of Duty to some extent followed these principles, but it was inconsistent. Moments with non-interactive exposition alternated with dynamic segments.
The Half-Life franchise still has many fans and some are still waiting for Valve to return with a full new episode (without VR).
There are modders who are trying to make their own "episode 3". For example, the authors of Project Borealis previously showed their work: