Hot take: The thing that makes Pokemon awesome vs all the dumb cyrpto clones of it is that you didn't have to pay to get the Pokemon you wanted with the money from your pocket.  You payed once for the whole game (and the selection of Pokemon in it) and then the in-game mechanics were enough to give you enough playtime for dozens of hours.

Would Pokemon would be remembered the same if in order to play the user had to fork over money for every Pokemon and every battle rather than exploring the map, battling trainers, and catching Pokemon as part of the payment?

I dunno, but it seems like the crypto knock-offs seem to think that their game will be the next Pokemon despite being heavily optimized for draining your wallet(s)... pun intended.