All of you whining about how you wouldn't be able to catch 'em all:

You would be in possession of devices which can convert such "monsters" into light energy and store it for indefinite periods of time.
Plus, they on average have human levels of intelligence and if you are good to them they are loyal, devoted and highly powerful creatures that can assist you with security, companionship, and you can be the one who guides them throughout life.
Also, the kind of shit you'd be seeing would be everyday stuff. Onix made an Earthquake? Deal with it. By common logic it would only be small-scale but highly devastating earthquakes.

TL;DR Man the fuck up.