Global inference is a nightmare, you simply don't want global inference. It means that the minimum understandable system is the entire system, if you don't understand the entire system you don't understand any of it, this can't scale.

When weird type theory people insist you want global inference and that you should sacrifice something you actually value to get it, treat them the same as if Hannibal Lecter was explaining why you should let him kill and eat your best friend. Maybe Hannibal sincerely believes this is a good idea, that doesn't make it a good idea, it just further underscores that Hannibal is crazy.