Actually it's because I'm considering it that I advocate this.
>How do you know you lost files?
You look for them and they can't be found. And keeping a tally and/or checksum per folder in your backup doesn't hurt either.
>Meanwhile if there's a synching problem and files get eaten by my file synching service Time Machine will happily assume those files were removed by me. One year later when I go to find some picture of my daughter I took and the file is gone you tell me what backup I go to to restore that file.
In your case it's simple, you can just go to Time Machine, as it archives all versions of the files, changed and/or deleted or not.
>You have 1 year's worth of hourly backups? I don't.
Actually with Time Machine you sort of have.
But, more essentially, you don't need "1 year's worth of hourly backups?", unless you're doing something very important and create new such files multiple times per day (e.g. if you're a business and store customer data, or a new site and you have your news database).
For stuff like "archived projects", "family pictures" or "music collection" just take incremental backups of them, and set your backup program to never delete any files during sync, but just put them in a "deleted" folder.
For stuff that changes fast, like working documents, emails and such, take backups with Time Machine (which happen in "real time"). Every few months take a full backup.
Besides network backup, never backup in just one external disk (and test your backup disks from time to time), and don't keep them in one place.
That is, if that stuff is very important to you. Some people can lose most of it, as it's mainly them hoarding digital BS.
If you're a business, OTOH, backup is PART of what you should do anyway.
If they rely on Dropbox getting syncing right to not lose "important files, photos of loved ones, ideas and important documents" then they are doing it wrong.
They should backup anyway, and only then trust Dropbox for plain syncing. Dropbox is not backup.