Any ramifications concerning the removal of PII is not the government's problem. If they can't use PII in a legal way, they shouldn't have collected it in the first place.
Not exactly... in fact, to the point that you're just spreading misinformation.
They didn't "deem the entire product illegal" at any point, and after OpenAI initially responding to Italy's objections by removing access for all Italians, they have since (a week ago) re-opened to Italian users having taken steps they presumably believe are enough for Italy to be OK with them operating there again.
https://www.reuters.com/technology/chatgpt-is-available-agai...
I very much doubt this is the last we hear from EU countries with regard to OpenAI / other LLMs and GDPR... but that's not the same as claiming Italy have already ruled it to be totally illegal.