... My concern is that this might be enough effort that people just won't do it.
There is no system imaginable that can be considered too easy not to do
. There will always be some reason in someone's mind that takes a greater priority than even scanning a barcode, I'm both guilty of that and witnessed it enough times (with great hypocrisy I probably called them out on it as well!) but even the simplest scheme has the potential to slip. So whether it's excel, paper, or a formal database, (as with so many things) its function can only possibly be as good as its measurement, how easily you can discover problems.
Based on a good system I once saw, the equipment was marked in some way to show it is 'from the shelf', a red tag or sticker or something with asset number and not easily removed, each user had a number of tags on elastic bands to attach to equipment when removed from the shelf. Any item then floating in the company was then both identifiable as needing a responsible person and having a responsible person. There was a general understanding that anyone had the right to restore the "ambiguous" equipment to the shelf. Each person had a limited number of their own tags, and longer-term "per project" ones assigned separately, different colors (maybe a symbol or shape in case of color blindness) per project or purpose maybe...
...it was only items that were formally listed as 'assets' or requiring calibration that had propper asset numbers, otherwise just had a shelf number and description, and things kept pretty much under control. I think it was just accepted that some things will end up in desk drawers no matter how its implemented, but it added that psychological step of "I'm taking this item, I need to put a tag on it else it'll get returned, best just sign it out also". It's pretty flexible and scalable.