For me The AG itself doesn't cause eyestrain as it is typically softer and it eliminates reflections which can really cause me issues. However Apple has moved to only offering AG on higher resolutions and higher DPI which can cause eyestrain.
Reflections tend to mess with your eyes. It makes them try to focus on things other than the text. I've always found anti glare to be nicer in this regard. I don't know how anti-glare could give you a headache. Typically headaches come from excessive brightness levels being kicked back at you from bright emitted + reflected light. I'm aware that they're not totally additive.
Weir question. People buy AG so they don't have to suffer eye strain.
As far as HD the higher res goes. People should learn that you can zoom any content. As far as menus and buttons go they are usually not too small unless one has mouse accuracy problems and/or badly corrected eye sight.