Synthetic (Dri Fit) polo shirts?
Yes, synthetic, Dri-Fit, micro fibre, polyester has indeed come a long way. They are beginning to manufacture the fabrics to feel more and more like cotton. In fact, I believe Nike has a "Dri-Fit Cotton" collection that advertises a softer cottony feel. Some of the other complaints about synthetics beyond comfort are the fabric's tendency to hold body odor. With cotton garments body odor will wash right out when laundered. You are correct about synthetics holding their shape though. They tend not to wrinkle either when removed from the wash, so it is really easy to care for. Whereas cotton, especially knits will tend to wrinkle and shrink in the wash. Points for that. Synthetics also have a bit of a sheen to it that some folks like. Typical cotton is more flat in appearance, but with certain higher end cottons, especially those that are mercerized, you'll get that bit of luster to it.
We have developed a couple of fabric technologies for our cotton garments that will give it similar qualities of Dri-Fit but with the comfort and and quality a cotton garment innately has. See image below of how our garments look after 20x washes. Similar to Dri-Fit, color and shape are maintained and it resists wrinkling, pilling and curling of the collar tips.
Also, we offer similar wicking or moisture management that Dri-Fit offers. That is our shirts will push moisture towards the outside of the fabric while at the same time spreading the moisture out for quicker drying. And of course, any odor will wash right out.
Hope this was helpful.