I thought about my discussion with my saxophone friend, and wondered what type of hosiery would suit her when she runs. Read the remainder of the entry to see my recommendation.
I think that it is a good thing to wear footless hosiery while running. It is a great way to keep your legs a little warmer, while removing perspiration. Hosiery can help you to be visible.
If your feet do not feel good with hosiery, when running, then I recommend wearing the footless styles with cotton socks. I am not an expert on athletic footwear, or even an amateur, so you should get your advice from somebody who actually runs, as well as somebody who actually conducts research on the topic, with a lot of random people to study.
In fact, I recommend that you wear footless hosiery and cotton socks, whether you are comfortable with only hosiery, or not. This is what I would prefer, because when you run a lot, you would probably rub your feet in your shoes, which would cause wear and tear on your hosiery. Also, hosiery does not have anywhere to wick the moisture away to, when it is inside the shoe. In other words, the shoe cannot get rid of perspiration fast enough, so a pair of thick socks would do the job better. Think of it this way, if you had to wipe a table, would you use a thick cloth made of spandex and nylon [and/or other synthetic fibers]? I would not, because cotton cloth's ability to absorb the moisture is what helps it to dry the table. The same could be said about fabric drying feet. Cotton keeps your feet dryer, when there is so much moisture that thin fabrics cannot wick away the moisture fast enough. Also, bear in mind that candle wicks are [or were?] made of cotton. So obviously, cotton can wick moisture. Am I recommending cotton all the time? No. I only recommend it when you have a lot of moisture that hosiery cannot wick away fast enough.
Bear in mind that I am not advocating 100% cotton socks. I am advocating cotton just in general. There are many cotton blend fabrics out there. Also, when I was in the army reserves, I saw people wear 2 pairs of socks. If I recall correctly, the innermost pair was a thin nylon sock, and the outer pair was wool or cotton.
Another advantage of cotton is that since it absorbs moisture, less of it will stay in the shoe, which leaves the shoe in a cleaner state.
In summary, do not throw away your socks, so that you can keep your feet dryer and your shoes cleaner.