I have had no problems in moving or fighting in turnshoes - in armour or out of it, for 5 years. It is a strongly held belief in many parts of the Western Martial Arts Community that turnshoes are essential to properly understanding the footwork in Late Medieval fechtbuch.In Late Medival Living History and Reenacment proper in the US, anything but turnshoes are forbidden by every 15th or 14th century group in these catagories actually attempting combat. Turnshoes are only particularly dangerous to wear in combat when shoes are mis-matched - that is, everybody in turnshoes are endangerd by the clod in Engineers boots. Getting stepped on while wearing turnshoes is not particularly painful if the person stepping is wearing turnshoes as well. Turnshoes that are broken in, and have properly abraided soles are no more dangerous in most terrain conditions than any other footwear, unless you start looking to athletic shoes with cleats.
In my experience, turnshoes are far more comfortable to wear than most modern, and most other tyoes of historic footwear. Ankle support can be got by a brace - ones are made that can be worn under turnshoes (at least ankle or calf boots). The dangers of turnshoes are highly overrated - largely exagerated by people whop have never worn a properly made set, or by people who just plain adamantly refuse to try anything 'less supportive'.
If your looking at combat in the SCA, or any similar club, then by all means where whatever you are comfortable with. In the US however, in Late Medieval reenactment, as stated before - no other type of shoes are allowed.
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Bob R.