I think a useful categorization of shime waza could be 1. naked strangles and 2. those requiring the gi to assist in the technique. I don't see a huge amount of benefit to an aikido person in learning and practising strangles that require either your partner's gi or your own gi to assist in the technique. It is unlikely that in a self defence situation you will either have to defend against a gi strangle or be able to use a gi strangle against an aggressor (unless in extremely cold environments). However, I do see a huge benefit in practising the naked strangles from the perspective of being able to escape them or not be caught by them and also to use them if necessary.
These are the strangles most likely to be used against you when wearing normal clothes. There really aren't that many naked strangles to learn. There are the two versions of the rear naked strangle called hadaka jime, there is the version of hadaka jime done from the front known as guillotine, there are variations of kata gatame which use your partner's own arm across their neck, their is sankaku jime also known as triangle which uses your legs around the neck and a few more such as anaconda choke. Just training in the naked strangles would save a huge amount of time and would add significantly to one's defensive skills and add to the repertoire of useful techniques.
In fact, I would love to see a form of randori developed for aikido which is done on the ground starting from the kneeling position, and using predominately wrist lock techniques, some elbow techniques from aikido, aikido face-down pins and only naked strangles. Styles such as Tomiki which already do two types of standing randori would probably be more receptive to this than some other styles.
I come from a judo background and have been in a "self defense situation" where I successfully employed a standing sankaku jime variation and gripped my own shirt the same way I would have a gi. I have also been choked unconscious with the t-shirt I was wearing in my younger years.
One of the biggest benefits of including strokes and strangulations in training is simply getting used to getting choked (mentioned earlier in this thread). Having been choked hundreds of times I can remain very calm as the "haze" sets in.