I think they did open a can of worms, but not that particular can of worms.
Star Trek had been pretty careful up until thenn about manufactured life: either it was an irreproducable accident or the results weren't sentient.
Or at least pretty close: Dr. Soong seemed to be able to reliably duplicate the process that made Lore and Data and Juliana, but he kept that information to himself.
This is because the ability to manufacture sentient life will significantly alter society, and raises lots of ethical questions.
So rather than deal with those messy issues, Star Trek chose to make tgat something looming on the horizon: were getting close, and we should probably be thinking about how to handle it when it happens, but we aren't there yet.
I understand why they wanted the mobile emitter for story reasons, but that's where it all comes off the rails. They wanted the mobile emitter to be a way someone could kidnap the Doctor or hold him prisoner, and technology doesn't really work like that. If the mobile emitter is capable of holding the Doctor's program and the ship's computer is capable of holding the Doctor's program, then there is no logical reason why they can't both do that at the same time.
So if the mobile emitter isn't just a remote peripheral of the Voyager main computer, then they could actually make copies of the Doctor.
And there you have it: even if they can't make other people like the Doctor for some reason, they've got a person they can make multiple copies of. And once Voyager gets home, they could make thousands of him.
As was suggested in Measure of a Man, every ship would have one. Two, ten.
Now, if the writers thought it was time to wrestle that issue, to look at how the Federation will adapt to being able to mass produce sentient beings, then I'll buckle up for that ride.
But they didn't want to do that. They wanted the Doctor to be able to travel to other ships and worlds without Voyager, and didn't want to address what that implies. They wanted bad guys to be able to kidnap him or hold him hostage without thinking of the technical problems with that.
They wanted to hold up a big sign that said, "The Doctor can't be copied but can move his program into other computers" and hope we wouldn't notice that makes no sense. Or think about the implications.
Star Trek has dealt with its share of unstoppable technological killers threatening to wipe out millions. It is well prepared to do so again.
But it isn't ready to face pointed questions about whether sophisticated holodeck characters like Vic Fontaine are actually slaves. And I'm not sure we're ready for it to do that either.