>So, when additional crypto supply comes on the market, the price of the original crypto, Bitcoin, falls.

This is often stated and completely wrong. Your misunderstanding comes from the fact that you think POW are done on individual Bitcoins transaction like it is done for the individual cigarettes in your analogy. In Bitcoin, the POW is done on the entire and complete history of the ledger since the inception of the Bitcoin blockchain. Thus a new POW on a block accumulates on top of all the previous blocks. When you create a entirely new cryptocurency, you are effectively starting with a POW of zero thus it has no value compared to Bitcoin which has years of POW validating its ledger.