You are absolutely spot on. However, there's one slight correction I need to make.
When you are given free flower gems, tickets (guaranteed), and numerous promotional opportunities to secure additional "freemiums", you essentially have more reasons to continue to play the game. With free flower gems, you get to perform 10+1 maybe 50% or 100% more often than you would as a purely free player on Nutaku's platform. While this doesn't guarantee you top girls, you essentially are given additional opportunities to try for them, which is still an advantage.