Think about it for 2 seconds.

There's many obvious excuses ...

Are you claiming a necessity ?

Free use without registration -> free to anyone and anything -> easy to abuse at scale, with no way to restrict use.

You can limit it a lot to minimize the abuse. In free entrypoint, set token and context limits to be very small. Limit to 2 prompts per IP or something every X hour. That is already a substantial limit where bypassing might not provide much benefits.

Residential proxies are too prevalent for IP address limits to work effectively.

You can use cookies to track usage history

I can delete cookies to obscure usage history

You can combine it with user PC fingerprinting

You can also just ask for a login…

You could also make the wannabe user buy a $500 retinal scanner and use biometric ID ...

Is there some public research that how often, for example, people download malware that allows this?