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.
Speaking of BACKUPS, in the Mac world one should be leery of using TimeMachine as a full system backup. TimeMachine does NOT backup everything. Passwords, logins, library authentications, etc. are NOT backed up as you'll find out when doing a full TimeMachine restore. All those need to re-entered. TimeMachine is extremely useful for file restorations, but if your system crapped out on you and need to get up and running quickly, then consider Carbon Copy Cloner which makes an exact image copy of system including all the password, logins, authentications, etc. My solution is to use both TimeMachine and Carbon Copy Cloner.