IIRC, EDI was shackled during most of ME2, only able to run the cyberwarfare suites.
We know she's hooked up to the entire ship, not just Cyberwarfare. I took the shackles to just mean that she isn't allowed to rebel or make decisions for herself outside of the parameters Cereberus laid down for her.
If we don't look at the endings, then there's no way to know that any of the endings will work how they do. That's an IT-like road we're going down.
Well I work in IT but I'm not sure what that means? 
In any case, we may not know exactly what will happen but, assuming we give any credence to what the Catalyst says we know that Destroy will destroy all synthetic life and, since it also goes on to say that Shepard also is part synthetic, this leaves open the possibility that anyone with synthetic upgrades (i.e. all biotics, most Alliance soldiers etc) will all die. Control, on the other hand, seems the least ambiguous result. Shepard is in control of what happens which is surely the best solution from Shepard's point of view.
Let me put it this way. You're on Rannoch, Legion's uploading code, and you KNOW Gerrel won't back down. Luckily, you have Tali, who can alter the code that Legion's uploading. Either you let one of the races die, or you have Tali alter the code so that, while the Geth each become their own unique identity, they're all subject to Quarian control, forced to spend their entire existence as slaves to a greater power.
Would you kill the Geth in that case, or force them into slavery?
Not the same thing. The correct analogy would be that it puts all the Geth under Shepard's control and that, not doing so will cause the destruction of both the Geth and the Salarians, for example.
And, yes, I see no problem with that. Particularly since the only control I would be doing would be to tell them to stop committing genocide. Other than that I'm happy for them to live full and productive lives doing whatever they want. Same goes for the Reapers.
Calling it 'slavery' or 'subjugation' is highly emotive language that really doesn't convey the reality of the situation.
Why care? Well, some Shepards are paragon, and they have strong opposition to slavery. See the Ilium Paragon responses, as well as Shepard's dislike of Batarians.
Unhappy is an interesting term to use. Personally, I don't think it entirely encompasses the feelings associated with having your mind twisted away from you, being forced to do things against your nature and having no escape.
Unless indoctrination just makes you "unhappy".
It's not slavery, though and it's not against their nature. Their nature is to follow the directives of the Catalyst who built them to find the solution to preserving organic life. It originally told them that was Harvesting but now there's a new solution to achieve the same goal. Their minds aren't being twisted and their nature is not being subverted. They're just being given new direction. And, even if Shepard was cruelly twisting their minds away from them and forcing them to live in peace against their will (which I don't believe is the situation) I still don't see why that's worse than the alternative. Better bad things happen to the bad guys than bad things happen to the good guys (particular since the alternative is the bad guys all die which is not exactly a good thing for them either!)