I absolutely cannot comprehend why a normal pokemon battling system wasn't included.

Because it doesn't fit the design of the game.

Pokemon Go is meant to be played while walking around outside. This means you can't have a lot of text because glare from the sun will make it too hard to read. The real battle system also requires more congnitive load than most people can handle while walking and takes too long which will lead to people stopping for extended periods of time at which point you're no longer playing a pedometer game.