The flights you describe certainly don't provide any advantage for turbocharged aircraft, but what you would likely find is that you would begin to make flights of longer duration and higher altitude simply because now you can. That three hour flight in a NA 337 at 165 KTAS now becomes a 2.5 hour flight at 200 KTAS. You save an hour of flight time on the round trip. That flight that you would've cancelled in your NA 337 due to bad weather? Now you can climb over the weather and be VFR-on-Top instead of either cancelling or sludging through the soup down low.
We tend to want to use our airplanes they way they were designed to be used. The short hops you describe won't hurt your turbos in any way, but when you do decide to fly farther, higher, and faster you will fall in love with your turbos!
Eastbound flights I usually go as high as I can, and I've seen 300 knot ground speeds due to the tailwind effect. Headed west, I'll usually stay much lower to avoid those same winds. I spend lots of time studying winds aloft before I file my flight plans.
Buy the best 337 you can afford, but to me, turbos are a huge plus!
We won't talk about pressurization, which I enjoy greatly as well!