If you think of it, it makes some kind of sence.....
First of all of course because the buyer pays for the notary.
Second, of "security reasons". Theoretically, seller can have "arranged" something with a preferred notary, so not all is correct.
Therefore, buyer chooses. As most buyers have no idea of notaries, that means buyers lawyer chooses.
And in 99,5% of cases, both lawyers are based in Chania, if the property is here, so notary also in Chania.
If buyer has a lawyer in Athen, seller in Chania, one have to travel. And as it is buyer (lawyer) who chooses........
For signing the contract, I would really recommend a POA, so the lawyer signs. The contract is in many pages, I have seen contracts of 40 pages, all in Greek of course. The one who signs, accepts the contract. The lawyer will understand the content, and is responsable if something is wrong there (and normally have insurance for this). If buyer signs, and not understand Greek, he/she depends on the translation from the Notary. When signed personally, and if something should be wrong, they are responsable themselves.
Normally, this is not something buyers/sellers think so much of, as all is arranged by the lawyers. So maybe Kilkis this is why the agent said that. Very often it will be the same Notary who did the last transfer of the same property, but not always. It all depends on which lawyers that are involved.
My wife and I last used a Notary when we married Greek Orthodox here in 2017. Recommended, and arranged by our lawyer. That will always be the preferred way, that when a lawyer is involved, they choose/decide. They know the notaries, and of course have good relationship with one.
And for Hector, if you have not signed a POA, I would suggest you do it. If nothing else, it will save you a trip to Athen at least, and also that the lawyer signs and therefore are 100% responsible.