To be fair, the platypus exists.
In all seriousness, anonymous, all of these are good questions, but it’s worth it to note that eggs work very similarly to poké balls. For example, a ponyta can emerge from a small egg because it exists as a half-solid, half-energy form until it hatches. This is why you often see a burst of light as the pokémon emerges: because upon hatching, it shifts into a completely solid form (or … you know what I mean, when it comes to pokémon such as gastly). Some pokémon tech researchers even theorize that poké balls were inspired by this process, as ancient poké ball craftsmen witnessed pokémon hatching and used apricorns and other devices to trigger a pokémon’s reversion back to this energy-based state.
Ultimately, however, which reproductive method an organism uses depends a lot on energy efficiency, and live birth is, in general, a very costly thing. That’s why pokémon lay eggs instead: as creatures whose lives focus on battling (another high-energy activity), it’s just easier for them to lay eggs than it is to undergo pregnancy. So I must say I respectfully disagree with your proposal, although it’s certainly an interesting thought nonetheless.