Why do blinds have two different close options

I have 2" blinds from Lowes, probably the same one. Our windows had enough over hang though. If I recall, there are little metal rectangle boxes that get mounted / screwed into the top of the window, and then the the blinds slide into the little metal box to hold it in place. These little metal brackets have numerous holes in them on both the side, and on the top. I think there were four screw holes, one in each corner on the top, and two on the side. If this is indeed the type of bracket your blinds come with, then you would most likely be able to get three screws in place (1 side and 2 in the top). Then repeat that with the other side of the blind.

This should be more than sufficient to hold it in place. I think it would look a little funny though, I would probably go with a 1.5" for looks. But you could use a valance to cover it up and no one would even know.

We have the exact same situation (bay window with 5 panes and 5 independent blinds) and I have toyed with the idea of mechanically ganging them all together.

The point where the twisting rod enters turns a cam which is coupled to a pulley system to tilt the slats. I posit that an appropriate line wrapped around each "twister" could do all of them at once.

I have not attempted it though—not even had a look inside. The set of blinds cost over $800 and my wife is quite reluctant for me to perform experiments which could affect the appearance or function. And she doesn't mind one bit if it takes me 30+ extra seconds per day twisting each individually.