Note that this isn't the primary function of Dropbox. As you know, the Dropbox site and apps are for syncing files to users and your other devices. However, there is a way using a workaround to keep your files only on the Dropbox site, to keep them safe online, and yet not take up space on...
I use Backblaze and love it. I never notice anything slowing down. When you sync for the first time, it will take a long time depending on how many drives / TB, but once it's done, it just sits there unobtrusively.
I also keep a backup on removable drives. This is a quick remedy if a drive goes down, or if I lost a file, but useless for catastrophe. So that's why I have Backblaze in addition.
I used to do the bank thing too, but it was just too much of a pain to go get them, sync, and then go back to the bank. Too much time went between syncs. So this other way works better.