Daystrom Institute

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.

TNG had the strong implication that holodeck technology was pretty new, in the first season, at least at that level of sophistication. The early holodeck appearances are practically gushing about how realistic and "real" they feel, in a way they really wouldn't be doing if they'd had that sophisticated stuff all their lives. If it was really only around at this level for a few years, it's understandable that they wouldn't be prepared for all the implications right away. Look how long it took for us to adjust to the printing press, and we're struggling with the internet right now.

The cool thing about the Doctor's overall personal arc is that I think most fans would agree that probably he wasn't sentient in the early episodes, probably was by the end, and there's no clear moment when it changes (although I submit the events of "Latent Image" as a candidate).

Something I think we're all learning now with the rise of LLMs/Generative AI is that one can perform the act of intelligent self-awareness without consciousness or understanding. Sapience without sentience.

Canonically the people in the universe believe that human like sentience is really hard to reproduce, thus they do not believe that it was possible even though it did happen.

I’d like to drop TAS’ ‘The Practical Joker’ into the conversation.

The simulators in the Rec Room of the 1701, seem to be a more basic holographic VR along the lines of Discovery’s combat training simulator that we saw Lorca use to put Tyler through his paces as a security officer in season one. Yet, the simulator was able to take control of the ship and advance its own objectives. It’s not as clear that sentience was achieved in The Practical Joker but it’s hard to argue that there’s no self motivation.

What the problematic Rec Room simulator in TAS has in common with the TNG holodecks is that it is integrated with the ship’s main computer. And unlike in Voyager (and Picard season three), TAS’ Rec Room simulator and the early TNG holodecks were fully integrated into and interoperable with the power supply, communications and other core systems.

I think the OP’s point that the integration of multitronic technology with highly advanced simulators may be one necessary element is fair. Combine that with access, integration and interoperability with the full resources of a starship, and it may be enough to argue that Starfleet should have considered the potential for holographic entities to attain some level of sentience.