I use a scoop of rye flour (30g) mixed with all purpose flour (70g) in my starter. The rye flour is like miracle gro for the bacteria. In my country it's also cheaper than all purpose flour.
Depending on where you are (I'm not asking) there are a few other flours that really work well as boosters besides rye. Buckwheat, Red Millet, Barley, Teff all work well.
To answer your original question I wouldn't bother using high gluten specifically for a starter. Whatever flour you normally use is fine.
I wasn't thinking of higher gluten in the starter specifically, but rather whether a starter destroys gluten to the point where maybe I should be using the cheapest option in the starter and not waste the flour that I will use later in the process.
I can't think of a good reason not to use the cheaper flour for your starter. In low hydration starters you still have some gluten, it doesn't really do anything for your bread though. High hydration does too, more or less depending on how much you use it and how often you feed it. Since your mixing it though you end up breaking pretty much all the strands.