First, let me say that on mobile devices, I literally loathe Face ID. There are lots of reasons for this:
- Fingerprints are just more convenient. Apple, for example, argued the false positive rate way too high. For me, as a user, I'm more concerned about the false negative rate. I think Apple just wanted more screen real estate. They could've easily put the sensor on the back (eg like the Samsung Galaxy S8).
- I have poor vision. I have to look at my phone close, same with my computer. And no this isn't an issue of better glasses or surgery. This caused Face ID to fail because I'm not in the expected frame. So I have to hold my device further away and try again. This is incredibly annoying;
- Touch ID has a much lower false positive rate on whether to initiate a check. That's because you've pressed the button. Face ID has to guess and it guesses wrong (a lot);
- I can't speak for other manufacturers but Apple at least puts in arbitrary security controls like N failures mean having to use my passcode many times a day whereas with Touch ID it's actually super rare;
- Masks!
- Touch ID isn't dependent on sufficient lighting
More context: prior to Touch ID I didn't use a passcode on my phone at all. It was simply too annoying. Face ID, for me, is too close to having to use a passcode too often.
I mention this as context for why I personally think facial recognition as an authentication tech is a terrible user experience in many, many cases.
Desktop is probably a little better because issues like your face not being in frame are going to be less of an issue. In my case I still have to sit close to the screen but my face is still within frame.
Phone manufacturers make this approach more resistant to spoofing by using other sensors. You say you've spent effort to avoid spoofing and hopefully that's true. I would be concerned that there's only so much you can do with a single vision camera and no other sensors.
Phones (and tablets) also have the advantage in they have a single manufacturer. Desktops are still put together with independent peripherals. That's... less secure.
Lastly, it's not a given that someone using a desktop or a laptop has a camera that's facing them.