Ascot Chang - have not gone lately but have read their prices now start at $1150. Personally I think you are paying their high rents.
Disclaimer - I own ZERO poly-cotton shirt, only natural fabrics for me. I also own ZERO non-iron shirts, personal preference as I have issue with all the chemicals they apply to the fabric.
I only wear cotton or linen shirts. I find they retain less heat than any blends. If I want to remain crisp all day, then I wear a cotton undershirt. The elbows and shoulders will wrinkle but that to me is normal. I find the weaves (slightly thicker) are less prone to wrinkles, but are not as crisp.
The biggest advantage of tailored shirts is you can get a high arm scye (armhole) which means there is less bunching of material underneath arms, a more tailored fit, and can get exactly what you want in terms of collar, sleeves, pockets (or none). I also get a slightly longer body so the shirt stays tucked, 8 buttons in front so less unflatttering exposure, a slightly larger left wrist so it covers the watch, and real pearl buttons for the added touch of luxury. You can also specify a different material to line the interior surfaces whcih show when the top button is undone or the sleeves are rolled up. Call me a shirt snob.