I am not sure how UA and UAX work in terms of facility leases and such (do the UAX airlines pay all the bills, and just get the per-flight check from UA), but if UAX does pay all the bills, then I imagine the only way those stations will get EasyCheckin is if they pay for it.

If UA picks up those costs, then large UAX-only stations might get them just for the fact they can reduce ticket counter staffing.