It's not the "wrong" way, it's just different. iMessage works well for businesses that want to create a conversational experience in their customer service that conveys care and attention
I suspect you are actually implying something different than conversational experience or using it as a substitute for a completely different concept.
What I don't understand is why a business would want to bifurcate their messaging stack... this is a solution that only works for half of their customers... for a business that doesn't have an app.