Is it recommended (or discouraged) to use a long therapeutic stretch band instead of a belt-style band for yoga poses? As an example, is innovation with the strap a bad idea, such as wrapping it around the heel in revolved head-to-knee pose?
There isn't much difference, and it depends entirely on what you want to achieve.
Straps are useful, when there is a static pose, and you want to "close the chain". For example, if you can't reach your toes while bending forward with good form, instead of compromising the spine, the straps add length to your hands and provide stability in the pose. A stretch band will also work for this purpose, but will provide slightly less stability. I use resistance bands in this way and the difference to using a strap is minor. Even if the yoga poses are static, they are usually active, that is, certain muscles are engaged, and both a strap or a stretch band will provide something to resist against.
The whole point of a stretch band is, that it can change length and provide resistance against movement. It is most useful if you have some dynamic stretches in your routine.