Preface: I'm not a dev, but I'll be hiring a good one to do the work.
I've seen tutorials that you can white label WP by making some changes in the functions.php file. I'm assuming that the white label plugins out there do the same thing, but without having to get into the code. Can you confirm if this is correct?
Once the theme is finished and white labeling is in place, the theme will be cloned for 20 different clients using InfiniteWP. Not sure if that makes a difference in your opinion, but I thought I should mention it.
The most important thing to me is whichever direction I go, that future WP updates don't mess up the white labeling that's been done. So, I wasn't sure if that means using a plugin is better or just having the changes in the functions.php file would be better. Thank you.