While they have a nice network, for a lot of destinations it involves backtracking. And other carriers in Europe offer flights to many of the same destinations.
Secondly, while they have recieved the last EU-Aid package , the economy and employment rates are not good. It's getting better, but demand won't be that high.
What destinations would actually require backtracking? I am not saying they are going to fly to Paris or Milan via Athens but destinations such as Istanbul, Izmir, Greek islands, Alexandria, Cairo, Beirut, Tehran, Tbilisi, Yerevan, Riyadh... could all be conveniently served via Athens in cooperation with Aegean.
Like I wrote earlier, additional feed on Aegean could help them turn this seasonal route into year-round. Don't forget that despite the ongoing crisis, Aegean remains an extremely profitable business.
I think that's what TK is for.
And how exactly is TK useful to United when they have a strained relationship and when UA doesn't even operate any flights to Turkey. Also, didn't UA's main partner LH suspend all code-share agreements with TK?
On another note, US carriers might be coveniently serving Europe and beyond through a few local hubs but they need to diversify their offer. If you look at UA most of their connections are through FRA followed by MUC.
In summer FRA turns into a zoo. It's not uncommon to sit in the plane for 40 minutes waiting for a gate. I was there about ten days ago and a United B772 was parked at a remote stand from where passengers were bused to the terminal. Once inside that overcrowded concrete palace you are faced with another mess and the fact that FRA is ugly and outdated doesn't help either (unless you are flying from the few fancy gates at the new terminal).
All in all, it wouldn't be unwise for United to look at other airports such as VIE or ATH to relieve some of the pressure from FRA. MUC is also great but its network and frequencies require some additional work.
Same applies for American Airlines which heavily relies on the overcrowded LHR. Then again, they don't have a choice as oneworld doesn't have another partner with a better location. RIP AB.
Delta is in the best position as they have both CDG and AMS which are both located at the very beginning on Europe and where they can make the most of Air France's, KLM's and Transavia's network.
So yes, maybe it's lucrative for them to rely on these few hubs but for some like UA and FRA or AA and LHR, it wouldn't hurt them to actually look at new ways to funnel their traffic as the overall travel experience can be quite bad and might actually push passengers to look at other, sometimes smaller carriers, that operate year-round flights to the US such as Norwegian, SAS, LOT, Finnair, Aer Lingus...