First of all, giving everyone a referral URL works great in a web only world but what if you're advertising on a Podcast (or gasp print or radio), is it easier to tell people to type in www.mysite.com/coupon to their browser or is it easier to tell people to enter COUPON at checkout?
Secondly, the amount of people who are going to have this adverse reaction to the mere existence of the coupon code field is vanishingly small. Most customers who don't have a code will just ignore it and move on (and actually many who have been told about a code will not even use it) only a small minority will bother searching for a code to enter when they don't have one.
Whatever web site had a coupon code field that made you this angry probably had at least 20 much worse UI violations they should prioritize above trying to eliminate the coupon field.