Then the gap gets bigger.
The wealthy didn't get their wealth because they are stupid. If competition picks winners, they will compete. If government picks winners, they will embrace power. And the surest way to hold power is to keep others dependent on government handouts, not dependent on their own abilities to compete.
We started our "War on Poverty" in the 1960's, when poverty was decreasing already. We had a solution without a problem, but it made people feel good to be doing domething. Government got involved, and now things are worse.