They work, but not for the reason you’re thinking. No doubt screens give off some less-than-ideal light, but that doesn’t explain this whole issue.
The main problem here is with the field of vision. I had a separate post about that, which you may want to go back and look at. Essentially, the broader your field of vision at any particular time, the more work your brain has to do to process the information. When we get stressed at work, we begin focusing on the entire screen, instead of the small portions of the screen where we’re working. And the bigger the field of vision, the more time dilates, so the faster you experience visual and mental strain.
It sounds minute, but it’s a big difference. At some point, they will make screens (hey, maybe they already do) that do not emit blue light, but it will not fix the problem. There are plenty of people that have worked in front of computers for years without major side effects. The difference is how they look at the screen, and perhaps how interesting their work is to them. Yes, boredom creates a strain as well,
So how do the glasses help? They restrict your field of vision. They make you focus on smaller amounts of the screen, which shrinks the amount of wasted energy your brain is using to process information. And the less wasted processing energy, the less stressed you are. And the less stressed you are, the faster your days will go by.
So get a pair, or don’t, just know that you can create the same strain without staring at a screen.