Lets try to convert my comments to a proper answer. First things first: The example you show was most likely done in a combination of After Effects and Illustrator. Mainly because the other motion graphics scream after effects and I doubt the operator would bother to learn yet another tool just for this use case.
So in order to use same workflow you need to in fact learn to use 2 software.
there must be simpler alternatives
No there don't need to be! Why? Well your needs as a animator are a bit open ended. As you said you could animate in power point but it lacks x,y and z. This pattern will repeat with simple software, complex software all the time. The reason you think that animating in power point is easy is simply: You already know how to use it and PowerPoint is a perfectly capable animation software*.
This will trump all other considerations. It does not matter how easy the software is, objectively, the use case at hand the best easiest software to use is simply the one that you know how to use. Everything else no matter how hard or easy seem like a bother since you need to relearn how to do basic things like text layout etc etc.
You can only overcome this if you invest time into it. But you go in blind, it may well be that a year form that investment you still think PowerPoint is the way to go.
I could control the next animation with button presses.
Its not that you couldn't do this in after effects too. You can record the button presses over time. Its just that an animator would probably not do it this way. Why? Well animation tools have to have a timeline. Recording the time is no different from going into that time and putting in a key frame. This is just as easy as choreographing the button presses but way more precise and flexible in every way.
It does not really matter what the software is. Unless its a real time rendering package then releasing on a key is not a benefit. They all have a timeline. Otherwise its just easier to do it the other way around and finalize the animation timing after the sound has been recorded.
There might be some tools available which teachers like me are not aware.
yes sure there are lots of animation tools out there but i doubt that you will find them easy. Simply because the another of relearning certain things, and relearning to think different is much work.
I mean if i had to do this i would animate in Maya, Mathematica, Toonboom or After Effects or Blender. Simply because i already know how to use them.
* Just a bit wonky form an animators perspective. But since you know this you should need to unlearn it first.
PS: Animation is hard work. Get over it.