>you can even program in a functional way without using them.
For a very tiny limited subset of programs. Anything beyond the most trivial of toy apps will use them.
>And also you can have languages which aren't putting the emphasis on FP at all and yet who have higher-order functions
Where their usefulness is seriously hampered by the language not being functional. This is the primary reason people think HoFs are no big deal. They've never gotten to actually use them in an environment designed to make good use of them.
For a very tiny limited subset of programs. Anything beyond the most trivial of toy apps will use them.
>And also you can have languages which aren't putting the emphasis on FP at all and yet who have higher-order functions
Where their usefulness is seriously hampered by the language not being functional. This is the primary reason people think HoFs are no big deal. They've never gotten to actually use them in an environment designed to make good use of them.