they should care, poisoning the well backstage is a good way to lose the goodwill you have with those talent and risk pushing them away with the competition. I'm sure AEW would love for Seth to get annoyed so they can make a big offer for example (theoretical, ofc).
there's also the bad press angle, which WWE has had almost none of since HHH took over. historically we already saw what Punk did to AEWs PR when things went south. And regardless if shooting would be dealt with immediately, the damage would already be done, so for me, that's not really a strong argument that is pro.
Money does absolutely not heal all wounds, or guys like Mox and Jericho would be back in WWE. Everyone has different motivations.