When should the Steady State Approximation be used?

In class, I learned that we should use the steady state approximation when there are multiple slow steps or if the rate determining step is not known (shown on this [Chem Libre link](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/04%3A_Reaction_Mechanisms/4.12%3A_Steady-State_Approximation#:%7E:text=The%20steady%2Dstate%20approximation%20is,a%20duration%20of%20the%20reaction.&text=Thus%2C%20the%20system%20has%20reached%20a%20steady%2Dstate.)).


However, further research (another [Chem Libre link](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/03%3A_Rate_Laws/3.02%3A_Reaction_Mechanisms/3.2.06%3A_Steady_State_Approximation)) shows that the steady state approximation is only valid when the second step is much faster than the first step, causing the intermediate to be used up immediately.


But isn't this just the same as assuming that the first step is the rate determining step? Why use the steady state approximation at all if it is only valid in cases where we could just use the more simple procedure arising from assuming the first step is rate determining?


