To my knowledge, they make money because they act like a credit card (they collect cc fee from the seller), but actually just proxy the charge to your bank account. You basically lose out on any your own cc rewards though since you can't proxy to another cc (then they would lose their profit margin paying your cc provider).
Personal example of when I found it useful: I used a burner card from them to buy a board game online, turns out the site was hacked, leaked the card info, additional charges were attempted but failed because the burner card settings only allowed the original charge through. Was really glad I didn't use my own cc.
If I need to setup a separate account to isolate privacy.com's use, why wouldn't I just make it a Citi account and use their virtual cards instead of providing all my identifying information to yet another third party open to hacking and diminishing of corporate values?
Are there any fees associated with that privacy.com service?