The point I'm making is that EU261 provisions should only be a factor in which flights to chose and remembering that only a very small number of flights qualify for EU261 compensation and a slightly higher number for duty of care.

I looked at June date for PHX-LHR

AA - 15.15 - 09.25
BA - 19.15 - 13.15

I'm certainly not going to wait for the BA flight just on the off chance of EU261 if I need to be in LHR in the morning rather than the afternoon.

And the OP is flying onto GVA and an early arrival there may be important to them.

The AA flight can get me (Via BA at LHR) to GVA by 14.20 but it's 18.00 for BA (using google flights)

If you have no time restrictions on where you need to be then sure stick to EU carriers but again I reiterate that it is a very small number of flights that come under EU261.

I'm not going to deny myself flight options on the off chance if my flight is delayed I might get some compo.