So Italy issued the ticket, gets my contact info from the rental company, then hands it over to the collection agency. Is it reasonable that all of that is something I agreed to beforehand? I have no idea. If you rent a car in the EU should you immediately send them a GDPR request after you are done to get them to remove your data so you can't be found? Or is there a legal requirement for them to hold on to the data? Are my rights different because I do not reside in the EU?

I assume (but I don't know) that GDPR applies fully if any party is in/from the EU. (In practice, if the data processor is outside the EU, enforcement might be difficult, but in your case it sounds like the data processor is inside the EU, so I imagine you have the same rights in this case as those who do reside in the EU.) However, my understanding is that

1) if your data is processed for contractual purposes, the data processor has a right not to delete it on request

2) if your data is processed for law enforcement purposes, the data processor has a duty not to delete it on request

There are several legal grounds for processing personal data under GDPR, and consent is only one of them. I think most of the others outweigh any request for deletion by the data subject.

Come on, GDPR does bot supersede other laws.

E.g. if some law requires a company to retain certain data for longer periods than stated in GDPR, that law still applies.