Anonymity is not binary. It's a spectrum. Phyical cash mailed to a company with only an account number is significantly more anonymous than a check or credit card they bill.

Perfect anonymity is probably impossible because information theory is impossible to escape. Which means you are trying to determine how far along the spectrum you can reasonably get for your particular risk profile.

Comments that pretend like perfect anonymity is the goal or act like it's binary are singularly unhelpful.