There's been many attempts at modding Half-Life: Alyx to make it playable without a VR headset, but frankly, so far, the results have been somewhat underwhelming. I think this will always be true to some extent, the mechanics of a VR experience are so engrained into the experience, but one mod is now getting to the stage where opinion is starting to turn.
The No VR mod from SoMNst has been slowly revamping the game's toolsets so that they make sense when played on a regular monitor, as opposed to a 3D, virtual reality experience. While a year ago it looked like a massive compromise, in the most recent progress update, things are starting to look really good.
The latest progress has revamped a lot of the animations and camera movements to make them feel a lot more like a traditional first-person experience, and it is starting to feel a lot like old-school Half-Life.
The game still has the issue of being far too slow-paced for traditional shooter controls, and so ideally, you'll still want to play this with a VR headset - that being said, if that is totally out of the question, this mod may be the gateway to making the game accessible to a wider audience of players. There's also a chance that, with more significant changes to gameplay and other tweaks, the experience could continue to improve and evolve.