Per the CONCORD rules, we would need to declare a war to shoot EM in high sec space. As for shooting them in lowsec or nullsec space. We do when we run into them, something we don’t very often do.
You’ll notice our low sec focus has shifted quite a bit to the caldari-gallente area or operation, at least based on CONCORD sanctioned kill reports. I expect recent development will only push things further in that direction.
This is a reflection of diplomacy from a specific Amarr group making it clear that operation there is only to be done under full subordination to them (Lady Yassavi was most direct in this) and of our Caldari allies being much better at communicating objectives and coordinating.
However, such a dominant group as Local is Primary with such a distinguished combat records will have no problem retaining full control of the amarr-minmatar area of operation from the disorganized and ineffective tribal militia. Indeed, where I to look at a map of control right now, I would surely see every one of those systems with a golden imperial logo above, correct?