Hey guys, I made an account just to reply here. I recently did a clean install of Big Sur on my 15 inch mid-2015 Macbook Pro because I was experience terrible slowdown. The clean install fixed those problems but all of the sudden Box Drive wasn't working anymore. I got the same "Please enable the Box system extension in System preferences..." message like most people here are familiar with - see screenshot. I followed procedure, went into Security & Privacy and even though I did not find the "System software from developer "Box, Inc." was blocked from loading." message with the "allow" button next to it, I did find another option saying "Some system software requires your attention before it can be used. -> Details..." option - see screenshot. When I clicked on that and marked Box, Inc. and clicked okay I thought that was all what's needed to procede. Restarted my laptop and then: nothing changed. I still got the same "Please enable the Box system extension in System preferences..." message. Tried this over and over, with also uninstalling Box through Terminal everytime - I did everything the right way, to no avail. UNTIL.
I finally figured it out. When the "Please enable the Box system extension in System preferences..." message pops up and it actually gives you a shortcut to your System Preferences, what it doesn't tell you is that you need to close the installer before making any changes in Security & Privacy. Once I closed the installer before I checked the Box, Inc. box in Security & Privacy -> "Some system software requires your attention before it can be used. -> Details...", an actual message popped up saying "You need to restart the computer for these changes to take effect". I did not get that message before. Restarted the computer and YES FINALLY: Box Drive install could be completed
I now have things running perfectly, like before.
Hopefully this will help a few people that have given up on trying. It seems like a logical thing to do, close the installer before telling your security settings that this particular program is safe - but as the message actually gives you a shortcut to the settings you just follow instructions and don't think about closing the installer - at least I didn't. I send my experience to Box and told them they should add the message ""CLOSE THIS INSTALLER BEFORE YOU MAKE ANY CHANGES IN PRIVACY & SECURITY" to their pop-up message. Hopefully they will take my advice