The ideal aperture is like really large, yes, a small F-number?

Depends.

Well then, at least in a portrait it is, yes?

It can be. But you need to think about this carefully.

Look at this image of some students who kindly volunteered the other day:

f/5.6:

f/3.5:

f/1.8:

f/1.2:

Which one do you prefer?

I think you may agree with me that a blurrier background is better. But so is a sharp face. Often, the extremely shallow depth of field (e.g. the DOF you get at f/1.2) is too shallow for comfort. Personally, I would say that for this kind of close-up hand-held available light portrait, f/2.8 to f/4 is great.