if you're using your wrist/arm/elbow to single tap you're doing it wrong. Just the fingers; that's how it works.
Think of it this way: you move one finger the same way you would as if you were streaming.
Practice this with both of your fingers and you can find your limit pretty quickly and train to overcome it.
Gotya Gotya Uruse (220 bpm):
https://osu.ppy.sh/b/76638&m=0This map is good to see how well you handle single tapping. In theory if you can easily do this with both of your fingers (single tapping that is) then you can stream at 220bpm. This can be applied with any bpm. Of course actual stream training would still need to be done, but it's still a good indicator of what you need to practice.
F.I. (180 bpm):
https://osu.ppy.sh/s/25828This is a slower map where the intro is another good indicator, if you can't even do this with both of your fingers then you need to practice it or play more 180-185 bpm maps.
More single tap maps can be found here:
https://docs.google.com/spreadsheet/ccc ... ring#gid=0Also, If you're not really noticing any difference try lifting your fingers higher. This will pose more of a challenge.
As for my thoughts on alternating, it's just slow streaming, so the concept and being able to do it isn't very difficult. I did it for 3 years when I started osu! and didn't see much improvement, 1 year of single tapping (still continued to this day) has blown away anything I did previously. I remember it was very difficult to switch, but very worth it.