As an aside relating to foot position, but not directly relating to an aikido koshinage, the basic hip throws I've been taught at a school of jujitsu involved having the feet close together (heels touching). The reasoning seemed to be that it kept your balance very much in one, small footprint; for a couple of reasons I could see and probably many more I couldn't.
Firstly, it made clear in the mind that the point was to be a pivot, in the way of your uke, so that they move over your hips (much like described by Ellis Amdur, in fact the basic throws were o goshi and koshi garuma).
Secondly, more technical leg-throws were taught further up the syllabus, where nage balances on one leg and uses the other to 'encourage' ukes fall by perhaps sweeping back and up taking the legs sooner (I think). These throws came from the same or similar basic posture, and being able to take one leg off the ground is much easier if your weight is neutral over a very small footprint: i.e. if your feet are already touching, you are more likely to have learnt a neutral posture and be able to take either leg off the floor quickly. This would mean you would have flexibility as to which technique to perform for a much longer period in the execution of a technique.
So in that particular school, with admittedly my take on some of the 'whys', the foot position made sense. What I took away from it is that in those throws, the feet being together wasn't specifically a technical aspect for those actual techniques, but good habits allowing for flexibility in technique later on. Which is a good enough reason to do those throws in that way. To clarify, I'm only a 5th kyu in jujitsu, I'm not claiming any vast knowledge or experience, just my own take
Aside complete, the koshi nages I've practised in my own school (of aikido) have the feet parallel, perpendicular to uke, and hip-width. Which makes sense for the way we do those throws. Foolishly I once though "ah! I think for hip throws the feet should be touching!" - transferring knowledge across arts without considering the actual reasons - and it didn't really help. The mechanics of the throws were different enough for the the hip-width posture to work better in those techniques from our school. Our style doesn't do many koshi nage, and so I can only say this observation applies to the specific techniques I know - but I think the point makes sense on a general level.
So, my take would be that for each specific throw, there's probably a good reason for the technical details encompassed in that throw, even if some aren't for the first reasons one might think.