Good job missing the point.

Bringing a Nocturnal AST with SCH just for heals would be the same as bringing a WHM that only used Cure, Cure II, and Medica, because that's all the Nocturnal AST would be bringing in equivalency; rather than bringing a myriad of HoTs and stronger healing CDs (CU). It's handicapping yourself and your group, for absolutely no reason. You continually dismiss AST HoTs as being ineffective in vacuum, on-paper scenarios before ever actually trying it yourself. In actuality, their HoT ticks are very comparable to WHM's, and Regen is the only HoT that WHM has that outpaces AST's HoTs.

At this point, it's a circular argument. If you enjoy handicapping yourself and your group by bringing NoctAST with your SCH co healer, then go for it.