Why doesn't Android have a built in task manager?
There is a so called task manager which you can find in settings labeled as memory where you can find all the running apps and their services and also check RAM usage for individual apps. There's another option labeled as apps (in settings) with options like force stop and uninstall/disable which allow you to kill and delete almost all the apps on your device respectively. You'll find option for managing storage used by apps which further allows you to clear cache as well as app data (Note-This one resets the app back to it's original state, proceed only if you are aware of what you're doing) You can also check the battery and data usage, app permissions (Marshmallow and above only), notification settings along with a few other useful options. Here's a screen shot of what it looks like-