PII that you don't need can become like radioactive waste. If it gets subpoenaed, and it comes out that you retained and produced it, your reputation may be hosed. But if there's nothing to produce, no problem.
That's actually not quite correct. If you're required by law to retain that PII, you'll be hosed if you can't produce it. But then, maybe you should be doing business in a different jurisdiction.
I'm thinking of Private Internet Access. To my knowledge, logs have been subpoenaed in two US criminal cases. And they just said that they didn't retain logs. But then, VPN services aren't required to retain logs in the US.