Yes the real reason is that it is useful/convenient, however this felt unsatisfying for me. So I tried to think what the most logical order would be if I were to decide. The hyperoperations build on top of each other. You know what 53=15 because you have it memorized but you can't compute it without doing 5+5+5. So let's say you had 2^3. To compute the answer you have to "unpack" it. 2³⁼²22=2(2+2)=(2+2)+(2+2)=8. As you see here, starting with the highest hyperoperation and working your way down is very naturally. So let's try it in an algebra expression with all the operation. 5+43²⁼⁵⁺⁴3*3=5+4+4+4+4+4+4+4+4+4. Slowly expanding until we are left with one easy to compute operation. Now let's test it with the reverse order of operations... okay I don't have time to finish the comment, I'll edit it, but spoilers, if you do it the manual way you need to expand and shrink it over and over and it's less clean imo