I don't know if that's really significant. But yeah technically you give up less information by using the card directly instead. But it's like going from 98% privacy loss to 99%.

Cash and Monero are private so they're in a different space and are what should be prioritized.

It's more difference than you think. Your card isn't logged into Google, Facebook, Signal and so on. It doesn't route through Cloudflare. It doesn't even connect to T-Mobile, Verizon, or Stingray automatically.