Why Agitate isn't used that often, all imo ofc:
The rules are unclearly written (some confusion regarding how temporary boosts to prosperity works)
There are extra rules for failure (failing by 10 leads to prosperity decrease)
Btw, this example isn't all that useful...
It doesn't go into holding advantage permutations (which is where a lot of players get lost, after what I've seen)
It says "realm action" when it's a regent action (only affects one province)
It does not take current prosperity into account.
It does not take blessings etc into account.
I am NOT trying to be obstructive here, but if you want the example to illustrate how it's done, it needs to be more useful.
That being said, I plan on agitating heavily each turn from now on, until all my provinces hit prosperity +2 / 9, though that is something that has been planned for a while.