sure, studying spelling is probably a waste of time with today's technology but that doesn't change the fact that he has a spelling test every Friday and he is going to feel better about himself if he passes vs fails. Its not a bad thing to set your kids up to succeed within the given system. Its fine to be a rebel but you must also understand that going to school involves testing and as a parent you don't always get to choose the subjects. I very much think that the self esteem my kid gains from getting good grades and actually learning to study is well worth the horror of having to spend a few minutes a day with his dad hanging out, practicing spelling, learning math and chatting about their day.
If you want to set your kid to succeed at spelling tests per se (and he doesn’t have enough past reading/writing experience to know the words already), you could get a list of likely words a few months in advance and put them into some kind of spaced repetition system (whether electronic or based on paper flash cards).
You’ll pay back your initial time investment within a month or two, and you’ll end up with a dramatic improvement to efficiency and long-term retention, as well as teaching a useful tool/skill that can be put to good effect if the kid ever needs to memorize trivia for med school or bar quizzes.
Trying to cram-learn a new list of miscellaneous things every week is a fool’s game. The key to human memory is connections, context, and repeated exposure, not brute-force effort.
Personally I always just read science fiction books hidden in my lap during spelling time in school, and my teachers gave up on trying to get me to study lists of words I already knew how to spell. My older brother’s strategy was to just do poorly on spelling tests because he thought it was a waste of time: never seemed to hurt him, and decades later he can spell as well as anyone. YMMV.