My criteria come down to the following:
1. It needs to be simple and kid-friendly. This is a kid's franchise, after all, so even if a Pokémon like Charizard is cool, it doesn't exactly strike me as approachable.
2. Its design needs to appeal to boys and girls alike. This is exactly why Clefairy was rejected as a mascot.
3. It needs to be at least a little anthropomorphic. Pikachu and Eevee have clearly defined eyes, mouths, and limbs, so they're easy to understand and relate to.
4. It needs to have overt supernatural powers. Growlithe is a much more attractive choice than, say, Lillipup, because being a Fire-type sounds much cooler than biting and tackling things like any regular dog would.
I thought about making Gholdengo the new mascot, considering how similar it looks to Pikachu, its friendly nature, and the fact that it's designed to be the "milestone" Pokémon. That said, the value of a milestone is diminished when it's everywhere.
I thought about a few first-stage Dragon-types as well, but none of them seems to strike the perfect balance of criteria I mentioned earlier. Dratini and Goomy leave too much to the imagination, Axew and Gible look too dopey, Bagon looks too rough and masculine, and Jangmo-o is overall unremarkable.
My tentative choice for new series mascot comes down to Cyndaquil vs. Riolu.
Cyndaquil is a simple, kid-friendly design with chibified limbs. I'd say Cyndaquil looks gender-neutral enough, and the fire quills on its back leave a strong impression; even if the fire comes off as dangerous, it can retract the fire anyway. My only real knock against it is that its eyes are squinted, so it's difficult to relate to Cyndaquil compared to the likes of Pikachu.
Riolu has mostly the same points for it as Cyndaquil, except that its design is much more humanoid, and I think it strikes a good balance between cute animal and relatable character. The only problem is that its aura powers are a little too hazy as a concept, so children will find it difficult to understand versus Cyndaquil.
I know these two choices are kinda random, but for my money these two have what it takes to be series mascot material.