Don't see it anywhere on the product itself but an embroidered logo on the chest would be a deal breaker
I agree too, and that's one bugbear I have with most current polos on the market. A cheap and obnoxious looking logo on the chest.
In fact what motivated me to produce my own line of polos was because of all the inadequacies and compromises with current polos. Not a single one I saw or felt was good enough in my opinion. So with my polos, I've set out to fix all the bugbears - among which include crappy fabric, naff logos, limp collars, poor fit and cut (so it doesn't stay tucked in) etc.
My polos are cut like shirts, with a curved shirt hem (we can do a straight hem if you prefer to have it tucked out, but I personally think it looks better tucked in), a yoke, finely-sewn side seams and fully pick-stitched shoulders and armholes (your move, Napoli).
Since you can't get polos or other clothes made from pique fabric done at a tailor (some do supply but they're all outsourced to factories), then the obvious choice is to search out a provider of polos of the highest quality. I hope I can rise to that challenge.
My embroidered Paladin Helmet is blind-stitched on the right cuff, so it'll be the same colour as the body of the polo. The short-sleeved ones will have the Helmet on the right bicep (that's where most folks who wear short-sleeved polos want them).
If the client requests, we can put the Helmet on the inside back of the polo, so it's not visible at all. But in the interests of brand integrity, we will not do a Helmet-less polo.
In Spore/Malaysia, I wear the polo with the cuff folded up to the elbow, so no logo is visible. Under a jacket, it's also covered. The polo cuff looks great with shots together with a Celadon watch, naturally