SNSD is the blueprint for hundreds of groups including BP as the original project was supposed to be YGSNSD but that fell through as trainees left or didn't advance the line up
Hundreds of idols have said SNSD is their fave or role model. Trainees are trained to match SNSD standard including ITNW being a common trainee song to practice.
They at the forefront hallyu across the world and put kpop on the map in a time when YouTube was still relatively in its early stages. If SNSD debuted in a time with social media they would've blown up when bigger.
They are multimedia stars, from day 1 they were getting multiple TV shows, guest appearances, high ratings, solo events like talk or radio shows. They were advertising monsters endorsing everything from typical fashion and beauty to electronics and homeware. They made a chicken franchise which seemed silly for gg to doing at the time and made become a multi million franchise
They were the face of Korea. Pop culture icons, tourism attraction, sent to inter national concerts as Korean reps, every CB they made national news.
In recent years ITNW is a defacto 2nd national anthem.
BP might have more success overall but SNSD is by far much more influential. Their impact evolved and shaped kpop industry and to and even Korea to an extent. Without SNSD inflence a lot of groups wouldn't have existed since and today and kpop itself would be different.