Well no, if rich people just consumed then the money would flow back into the economy via their consumption. This would generate economic growth. Whether that growth is greater or lesser than their capital investments would presumably be hard to measure. But to assume growth resultant from investments will always exceed growth from consumption requires evidence.

Now an even better outcome would be that rich people didn't get rich in the first place. This would mean lower inequality, which in the data correlates with higher growth. This is demonstrated convincingly in Piketty's work.

Overall, if youw ant to maximize growth for the poor (or really, growth for all of society at an equal pace, say), then you would want to dramatically raise taxes on rich people and eliminate the class entirely (IE, no more rich people). That would massively stimulate growth and of course skyrocket the wealth of currently poor people.

It's a bit sad that the solution is so simple and has no downsides.