We're taught, from an early age, that this is the proper configuration for a current source:

and that this is the proper setup for a current sink:

But what if instead we use this as a sink?

and this as a source?

Question 1: Will these alternate configurations work?
Question 2: Will they work, but with some deficiency?
I'm really not trying to stir up a hornet's nest here: I'm just trying to wrap my head around this basic electronic concept.
It seems to me that really, either way should work, because if we think of the transistor as a device that passes current through from collector to emitter (conventional current flow direction, not electron flow), similar to a valve with some fluid flowing through it, why should it matter whether we tap the current at the top or at the bottom?
Now there is the matter of base current, which flows out of the emitter of the NPN and therefore adds to that current.
However, I
B is so small compared to I
E that it's basically "swamped" and can therefore be ignored, right?
This is basically the same as the high-side switch vs. low-side switch thing.
Just to be clear, I am excluding applications like precision current sources here; I'm proposing a typical current source that's just accurate enough.