It was never too difficult on desktop monitors, but they were ubiquitous on laptops at one point. I suspect the thing about reflections is because so many people encountered them on low brightness, low quality budget laptop screens.

Glossy screens are not reflective with suitable ambient lighting. The same screen brightness does become difficult to view at lower ambient light levels than matte screens but for a desktop monitor in a controlled environment that's not necessarily a drawback.

The anti-glare coating works both ways, so the benefits of not having it are that the picture looks smoother and general better when the light levels are correct.

They're less popular than ever though, even those manufacturers that used to favour them like Eizo have swapped over to matte.

Your best bet right now is probably one of the low haze anti-glare coatings (dubbed semi-glossy). I know some of the big screens with VA type matrixes use it.

I'm not familiar enough with the science to debate it, but when it comes to ambient lighting - certainly in the workplace a lot of people want to let the sun in. It was really depressing for my first job where we had big CRT glossy screens, and all the blinds had to be closed, all day. Ambient lighting is no match for some nice daylight, and now when we open the blinds, unless there's direct sunlight on the monitor, we're fine.

You can have a gloss monitor that can have anti glare on it, I remember Asus made one and I had it long ago and had a coating but was still glossy not as glossy as glass but still noticeable to see yourself.

anti-coating has come a long way my friend :)