That's called cabotage, and it is not allowed by the US. Although US airlines are allowed to make stops and pick up passengers at multiple points in the EU, EU carriers are not allowed to fly between multiple points in the US.

That is why you will find no European (or British) airline operating between different US points in that manner.

I'm not certain that both the US and Canada would allow any and every foreign operator to perform a "transborder" flight like that. While they were relatively more common in the past, there seem to few left these days. Cathay Pacific used to have a flight between JFK and YVR which they wanted to bring back after Covid; however, the mere fact that such a "transborder" flight was once allowed should not be taken as meaning that Aegean would also have such options. It is far more likely that Cathay and Hong Kong had a special clause in whatever ASA applies to flights between Hong Kong and US/Canada. No European (or British) airline that I am aware of operates such a transborder flight and I am not aware of any clause in the EU-US open skies that would address such flights (which would also require Canadian approval).

When it comes to operating routes, you cannot just assume that an airline can, or will simply be granted permission, to operate routes at will.

I can guarantee you that Aegean would not be granted permission to operate between NYC and ORD. The only example in recent times that I can think of was Qantas, who used to operate a flight between NYC and LAX en-route to Australia. However, they could only pick up passengers in JFK bound for Australia - nobody could disembark in LAX. And again, this right arises from a specific ASA or grandfather right that Australia/Qantas had, which is not available to Aegean.

Widebodies in winter!!! When demand for flights to Greece is at its absolute lowest! That would be a disastrous business case for buying a widebody fleet.

There may also be issues regarding their slots at LHR - you cannot just decide on a whim to replace an A320 with a widebody; and then there are questions regarding your other slots. Do you combine your 3 or 4 daily scheduled flights into just one single daily rotation operated by a widebody? What would happen to your unused slots? You're going to lose them if you don't use them. Are you going to be able to lease them out for a short, mid-winter period? Or are you going to run all of your 3 or 4 daily flights anyway, with one (or more?) being operated by widebodies, thereby further increasing the number of seats on the route, which will only have the effect of further depressing your revenues? (With so many extra seats to fill at the quietest time of the year, you'll end up giving seats away at a pittance, and still have half-empty planes)