I recently had a case with one such services. They store personal information that could be very damaging if it got out. SSN, driver's license, name, address, phone, credit card info, etc.
I decided I no-longer needed the service and so I asked to close the account and clear all of my data from their servers and backups. I was particularly interested in the information that could be used for nefarious purposes given a data breach or a sale of the business.
They refused and gave me some bullshit reason.
I moved immediately to arbitration per their own TOS. Within a couple of days they became very responsive and have, in theory, cleared all my info from their service.
And that's the issue. How do you know? They could have lied to me just to get me to drop arbitration. Hard to know how far to pursue something like this. No company should keep information on you that you do not authorize them to keep. A consumer ought to have the right to have any and all traces of their personal data erased from databases with absolute certainty. Privacy ought to supersede everything else.
What if you want Facebook to clear all data related to your account? I don't think that's possible in the US, is it?