You are also helping them by reminding them of exactly what skills you want or what you bring to the table, which may jog additional details loose in their memory.
And I was asked to do so. Usually within 5 minutes they acknowledge receipt and send it.
The prof signs it once, you keep it forever.
This methodology works (very well) for me. Perhaps I do not submit references to people who think I am lying directly to their face, or perhaps you have tried this in a low-trust environment where it was not allowed.
Once you graduate and start working in your chosen field, those reference letters will be out of date in a few years, as propective employers don't give a hoot as to how well you did in your 2nd year data structures course. If it's for grad school, then it will be as I said in the vast majority of cases: A direct request soliciting feedback to the faculty member based on credentials you provide.
I don’t know too much about “grad school” unless you consider law school graduate school, and then I can assure you that zero direct requests soliciting feedback from any faculty member were made during my application process.
I admit that very occasionally someone wants a directly submitted recommendation. When this happens, I email the old recommendation to the old recommender and just ask them to resend it.