I don't know that there is a direct correlation between tire lifespan, age and harshness. Certainly, a tire with full tread is a bit squishier to a sensitive driver. And maybe quieter, due to no unusual wear patterns having developed yet.
However, the idea that the sidewalls become markedly stiffer and therefore harsher with time is not something I see on the Michelin tires I typically use. Maybe on lower quality tires, this is a "thing". One thing that could settle the issue is hot day vs. cold day and/or driving hard enough to heat up the tires, and thereby soften the rubber a little. Seeing if that makes a big difference in ride quality.