The video below demonstrates my ideal and efficient method for storing board game components and for starting the set-up process ahead of play. I know some argue that time spent bagging components allows for faster set-up during the next game, but I don't think that's true, and I plan to record side-by-side teardown and set-up videos in the future to demonstrate how my approach takes less time.
I do bag cards in most games as I don't want them to be bent or marked, but in my experience other components are not damaged by leaving them unbagged in the box and game boards are not warped or damaged by resting atop unbagged components. (The only time I recall having a warped board is in my copy of Michael Schacht's China — and that's because the pieces are bagged, yet the bag isn't large enough for all of the pieces to lie flat, so the board was resting on a few protruding bits. An unbagged copy of the game would be a better condition today!)
Note: This method is not approved for use on games in the BGG Library, and I have been reprimanded for showing a BGG Library game that is not fully bagged. I do not transport thousands of games in a semi, but few people do, so I don't think the requirements of a library are necessarily the best requirements for individuals.