This seems like a good teaching tool, but seriously would anyone want to write out big equations with the triangle instead of x^n ? Powers are used incredibly often and the standard notation is clearly easier to write in both typing and handwriting, and the same is true for log. And as has been mentioned the n-th root symbol is technically not a true extra notation, as you could always write x^(1/n) - but it does make some equations extra clear because there are so many roots that often need to be taken.
So, don't complain about the notations - the triangle would be far more annoying to write equations with if that's the only thing you use. The notations are like 'helper' functions that make implementing a larger function easier, but also make things less clear to start out with because there are more forms of the same thing - so use the triangle to point out it's all the same thing (or all related, anyhow) but keep the notation all the same.
So, don't complain about the notations - the triangle would be far more annoying to write equations with if that's the only thing you use. The notations are like 'helper' functions that make implementing a larger function easier, but also make things less clear to start out with because there are more forms of the same thing - so use the triangle to point out it's all the same thing (or all related, anyhow) but keep the notation all the same.