This is a leftover from the days of big radial engines. There is a lot of highly loaded metal moving around in a big twin/4 row radial and there was plausible evidence that there was more probability of an engine failure at the first power reduction after takeoff than at any other point in the flight. Failures of the engine reduction gearing seem to be a common failure mode.
However for modern piston and turbine engines, I believe no one has been able to demonstrate an increased risk of engine failures at the first power reduction