As the final evolutions of Charmander, Bulbasaur, and Squirtle, it makes sense that those three Pokémon graced the covers of Pokémon Red, Green, and Blue, respectively. You could argue that the actual starters were the more logical choices for the games’ cover stars, but the final evolutions of those creatures not only look better; they helped convey the idea that the first Pokémon you see in the game are going to evolve as you progress.
However, the fact that those three are such logical cover star choices only makes it that much more confusing that none of those Pokémon were chosen as the series eventual “mascot.”
There’s certainly a strong case to be made for each of those Pokémon becoming the eventual mascot. Bulbasaur, for instance, is not only the first Pokémon listed in the Pokedex, but Pokémon composer Junichi Masuda says that Bulbasaur is his favorite starter Pokémon because his unique look makes him a “very Pokémon-like Pokémon” who exemplifies the unique style of the franchise.
Squirtle/Blastoise would have been an interesting choice if for no other reason than the impact of Pokémon Blue. Not only was Pokémon Blue the upgraded (arguably definitive) version of Pokémon Red and Green in Japan, but “blue” was chosen as one of the colors for the franchise’s U.S. releases due partially to the belief that blue and red could remind American gamers of the U.S. flag’s colors. In a way, then, you could argue Squirtle was believed to have international appeal.
So far as starter Pokémon go, though, Charmander/Charizard may have the best resume for future mascot status. His powerful design has long made him an instant favorite amongst some fans, and he’s the only one of the starter Pokémon to appear on the covers of both the Japanese and international versions of the games. He also embodies the “dinosaur” look the Pokémon team was originally going for during the early creature design phases. For that matter, Rhydon could have been the mascot as he was the first Pokémon designed for the game, and statues of him even appear throughout the original titles.
Ultimately, none of those Pokémon were chosen as the game’s mascot, and it’s still not entirely clear why. However, the simplest explanation is that the Pokémon team wasn’t thinking about having a “mascot” during the series’ earliest days and didn’t pick the starter Pokémon or the cover stars on the basis of their viability as eventual icons. Simply put, they weren’t thinking of Pokémon as this potentially global franchise that would impact the industry for the next 25 years when they were still just trying to finish and tweak the games.