My understanding of the Mosquito is different.
They were not great fighter planes and did not deliberately engage in combat with ME-109s.
Their light weight gave them one big advantage: they could fly higher than other planes, and usually stayed out of the reach of both German fighter and AA fire.
The limited bomb capacity meant that they were not a major bomb threat, but the "pathfinder" role served the bigger bombers well.
And the pilots loved flying this plane. Not getting shot down as often might have been part of the reason.
The Mosquito was one of many technological changes in warfare that happened in WW2. It's kind of hard to claim that it changed the course of history by itself.