Being a literal-minded person, I don’t venture into analogies much, but I’ll try one here. This question of engineering versus trial and error (guess and check) is comparable to how people learn software or home appliances or electronics. Unlike most people I read the manual. It’s amazing how much you can learn that way and it’s far more efficient. But what most people do is a just dive in and try things, or they simply remain ignorant. I read the manual and find out all you can do (if it’s a good manual) that most people who just dive in and try things are not going to figure out.
The engineering style of game design is like reading the manual, the trial and error style is like diving in and trying things. It’s much less efficient, but it is easier, just like not reading the manual is easier, and we can apply this to games. I would rather read the rules to a tabletop game in order to learn it, unlike most people who would rather be taught. It may take longer, but I miss less when I read the rules and understand the game better when I read the rules, if they’re good set of rules, than when somebody teaches me.