Every competent woodworker does stuff that is at least as intellectually challenging as routine software development. But you don't see a lot of people saying "few are smart enough to cut mortises and tenons".
I remember about 20 years ago being just fascinated by the folks hired by my dad who came to do construction at our house, the key thing I learned watching them was that you needed the right tool for the job at hand (and you don't even have to own a lot of it -- you can rent from Home depot a lot of the big tools).
Insofar as smart coders are good engineers who know what tools to use and follow directions, they'd be pretty good at it. I do most of my car work in my garage myself, and I'm planning to build a room in my basement next year myself. Not only is it not that hard, it's actually extremely fulfilling and fun to do it yourself.
Watch someone hand-cut a dovetail (heck, watch 10 different people hand-cut them), then get a chisel and a coping saw and a marking gauge and try it yourself. It is not easy, even if you (as I did, to little effect) condense all the video tutorials you watch and the chapter in the Tage Fried book into written step-by-step plans.
You can absolutely do it! I'll eventually be able to do it semi-competently, I think. But I doubt you'll get there without learning to respect the challenge at least as much as you respect the work that went into getting you to a comparable level of coding aptitude.
Isn't every engineering job essentially applied physics?