i.e. if anything north of Antalya has no more connection to the Mediterranean or Atlantic Ocean (i.e. access to the sea) without going through Greek waters, that's an issue for Turkey. Greece already 'owns' about 50% of the Aegean, 12nm would extend that past 70%.
International law is the area of law least concerned with morality. Everyone disagrees but that's how it works because there's no such thing as a world court, world government, world police force. Just some semblance of it in our institutions that make a good effort but where political power is still key. Greece doesn't come close to Turkey's geopolitical power and has no explicit support from any major powers on this issue. That's why it hasn't changed from 6nm despite the law.
I would disagree by the way that they don't have valid claims. Perhaps under strict application of international law (which doesn't really exist) they'd lose. But they also make non-legal claims to equity and make claims about genuine concerns of the so called greek lake, which make quite a lot of sense.
Let's just assume that it is.
But you'd have to agree also that's hard to have much sympathy for Turkey as the victimized party in the region. Or to repurpose a quote from Apocalypse Now:
"What do you call it when the bully accuses the bully?"
Turkey should have signed UNCLOS a long time ago. 168 countries have. The only reason they postpone it is to maintain claims over Greece. Signing UNCLOS would also mean that their warships can no longer venture near Athens while claiming to be on international waters. And of course they'd finally have to stop pretending that the Greek-Cypriot EEZ connection doesn't exist.
I can see why Turkey and China are abusing historical data, archives, archeology, myths etc, just like you said, but I can't help but notice that they don't have any valid claims, and the moral thing to do (if there is one) would most likely be to drop those claims.