So the guns are just a tool after all. The army isn't leading the rich because it's the rich who built the army. It's the rich who create the wealth and the guns.
> It's very simple: a handful of wealthy people can never be a match for an army of people with guns
It's simplistic. The only example you came up with just showed an error in judgement on the part of the rich due to lack of experience (some things were unfathomable for them), not a failure of wealth to give you that power. Both wealth and guns can "explode" in your face if mishandled.
Insisting the French revolution is the only true evidence that wealth is worthless in gaining power is like insisting the thousands of accidental gun deaths are the only true evidence that people with guns will just accidentally kill each other.
As you can see from today's situation those people with wealth learned from the past. They know where to push and where to pull in order to successfully keep power. They have refined the tools they buy with that wealth. And the civilized world has been managing to keep going this way without using a gun (well, not on home field anyway) for the longest time in history. A library will do a far better job at making my case than I can do in a comment. I strongly encourage it.