this is exactly how all ponzi-like schemes operate. Bitcoins is simply a classical ponzi-like scheme
You keep using this word. This word does not mean what you seem to think it means.
A Ponzi can not operate if nobody new is recruited. Its very existence depends on a continuous flow of new participants.
Bitcoin does not need any new participants at all. The existing participants can pay each other with bitcoin and it will operate just fine.
What's the difference between new participants funding existing participants, and existing participants funding existing participants? There is none. In both cases, participants are not paid by scheme organizers or scheme's economic activity but from funds brought by the participants themselves.