In the age of social media, delayed gratification is an endangered species. In the age of Pokémon Go -- well, it's practically extinct. But if you're disciplined, it's still the best way to get where you wanna go -- namely, to level up in a hurry.
As detailed in a recent YouTube upload by MoreAliA, the higher level you achieve as a trainer, the higher CP the Pokémon you encounter in the wild. That, in turn, means wild Pokémon will be trump the Pokémon you've been carrying around, and you'd be wasting your precious Stardust on Pokémon with lower ceilings. As an example, host Ali-A explains that his starter Pokémon, a CP 13 Squirtle, immediately becomes meaningless when he catches at CP 113 Squirtle in the wild.
Additionally, you'll spend more time at each subsequent level, since each level requires a progressively higher XP, and using your Stardust on higher CP Pokémon means it'll have a much higher ceiling.