To add to this, we have to remember that Multitronics isn't the magic formula on its own. In TOS: "The Ultimate Computer" Daystrom couldn't get it to work - Units M-1 to M-4 were in his words "not entirely successful". The breakthrough of multitronics as embodied in M-5 was the ability for the system to be overlaid with the engrams, personality and, fortunately, morality of persons.

Daystrom used his own engrams to bring M-5 to its full potential, and his anxiety and fears about wanting to prove himself and survive academically translated into an obsessive drive in M-5 to also prove itself and ensure its own survival. Luckily, Daystrom's morals also translated over, and so M-5 was forced to confront the moral implications of what it had done, eventually electing to terminate itself in atonement.

When Zimmerman created the EMH, he incorporated part of his personality into the program, so it made sense to use multitronics because the technology had the ability to do just that. DS9's "multitronic engrammatic interpreter" is an offshot of that tech, and one imagines from the name it would copy a person's engrams in order to process and manipulate it.

So while it may have been obvious to us that sapience would arise from using multitronic tech in the EMH process, multitronics by itself won't do that. It's when you use it to incorporate real people and memories into its matrix and let it percolate that the potential arises.