Why does the institute make synths?

Without going into spoilers, when you meet a certain character, he explains:

... Scientific curiosity, and the goal of perfection, drove them ever onward. What they wanted was... the perfect machine. So they followed the best example thus far - the human being. Walking, talking, fully articulate... Capable of anything.

So it isn't to be slaves or to carry out cheap labour - It's just out of simple scientific curiosity and basically playing God.

This might contain spoilers, be aware:

• I do not think Gen 3 Synths need food and sleep. While they look and behave like humans, those are still machines. They probably CAN eat, but they don't have to.

• Human resources are limited and have to be trained. Most of the raiders where just reckless and brutal, not capable of solving complex problems. Synths can do that.

• While you say humans aren't as loyal as synths, synths still are more loyal and can be developed further. You can tune a machine until its perfect, which was the goal of the institute.

Humans require years of development before they can be used for any extensive labour, and it is easier to rationalize owning someone when they are not human (that is not possessing your sapience) and can be programmed for a particular task, not to mention humans sort of... resist being captured.

Also,

I suspect synths were further developed to secretly maintain contact with the surface after distrust from the surface folk forced them underground.