From an engineer's perspective who may be interviewing you...how am I meant to evaluate your skill or see how you solve problems if you refuse to do so in my presence?
Let's not mince words here. I suck at interviews. I was unemployed for about five months because my interviewing was so terrible (from my perspective; I know I'm a brilliant developer but interpersonal communication has always been a weakness of mine).
But that didn't mean I didn't do any coding exercises; quite the opposite.
I made sure that I met their coding exercise requests, and showcased what I had learned from past experience (including clear documentation of code, READMEs, unit tests, etc). I wanted them to know what they were getting from hiring me; a diligent worker who regarded themselves as a professional and expert, and one who understands what it means to architect the solution, test it, and deliver it in a way that makes sense to everyone.
By you refusing or failing to do that, you miss the opportunity to really put yourself out there as a stand-out candidate. I've not heard of many professional institutions hiring someone without asking them some kind of coding exercise. Let's face it - as a developer, you're going to be paid a lot of money to solve problems, and if you don't showcase how you solve (or at least approach) problems, you're not showing me that you're worth what I'm willing to pay, or more.