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 used Rye to start my starter. After about 2 weeks I then just fed it white bread flour to maintain.
I think once you have an active starter i.e. active bacteria, you can feed it any flour+water. I used a 1:1:1 ratio.
When making my doughs I would use a variety of flours for flavour/texture.
Ok - I have always used unbleached all purpose flour in the starter and thought it so unfussy I didn't worry about the brand until one time my husband got store brand all purpose flour, and my bread was struggling, it took me awhile to figure out it was the flour! So some all purpose is so low in gluten it's almost cake flour. Now I am more specific when I ask for flour, but Gold Medal or King Arthur all purpose unbleached work so well to keep it healthy, I do not use bread flour or whole wheat. Used to have a rye starter but this one is so much healthier and easier to use - it's all purpose starter!
I use pure bread/high gluten flour for my starter. It makes it so I don't have to think too much about it, and I do a no-discard system, so it's not like I'm wasting any of the more expensive flour.
I use normal flour for normal feeds, and then I'll use a mix of the flours I'm baking with when preparing a levain. Not sure it does anything, but it feels "correct" somehow.