>This is the most over babyface stable in the company
That's kind of the problem. The whole concept is basically a heel stable idea, not a face stable idea. Faces don't just kick the crap out of people for fun, but that's what they are doing. But who are they going to kick the crap out of other than weaker faces? See below.
>Why aren't they going after the top heels?
This is a problem with AEW being a free-for-all booking wise - it's hard for things to come together. The Elite are the top heels I suppose, but they are busy doing their own story arc which won't be over for months. MJF is also a top heel, but his program with Wardlow is just starting. The Jericho Appreciation Society could be an option, but again, their program with Eddie/LAX is just getting started. Team Taz has been jobbed out to midcarders since the start and has little credibility despite everyone being ready to buy them as credible. Dan Lambert's group has already lost to everyone.
