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Some people deal with confidential files and use Dropbox for these. It would be very useful to allow people the option to clear their "Recent" files at will to allow more privacy and discretion.
It's so, so much better on mobile where you can assign a passcode or in the case of the iPhone, fingerprint security, to even Open the Dropbox App. So, they obviously think that someone being able to access a user's files without their permission is an important security risk.
Why would they just blatantly display your recent or most commonly used files on a desktop or latptop computer, where you can't even put a passcode on Dropbox, and give you no option to disable it? Basically, if I get up from my comptuer without locking it out, and someone happens by and opens up Dropbox, they can see what files I've been working on; often sensitive information. Windows has the ability to turn off tracking recent files/folders, so does almost every other program.
If you're going to include the recent or common files/folders feature without a way to turn it off, you need to add the ability to require a passcode to access Dropbox just like on mobile.