This is complete and utter nonsense. First of all,
and this has been beat to death here repeatedly, your car actually uses no gas when decelerating in gear because the fuel injection system shuts off the fuel injectors completely in this situation. Idling in neutral uses gas. Still, I doubt you'd notice any difference in fuel economy.
Oh, and you put far more stress through the drivetrain and suspension under acceleration and cornering than you do while decelerating in gear. If you think you are saving wear on your car by coasting in neutral you're nuts. It is neglible.
When I drove a MT, and I did for nearly a decade with 2 different cars, I would downshift maybe to 3rd or 2nd but almost never into 1st, sometimes not even to 2nd, depended on how lazy I was feeling at the time. I would coast up to a stop and if the light was long I'd leave it in neutral until the light was about to change. If it was short I'd put it in 1st and wait in gear until the light changed.
When just cruising I would always be in the proper gear, uphill, downhill, flat surfaces, always in the correct gear. Never did any coasting to "save wear" on anything, any coasting in neutral I did was approaching a stop and was out of pure laziness, nothing else. Only thing I ever replaced was a clutch (and throwout bearing for good measure) after about 60,000 miles. Never wore out an engine or motor mounts, or transmission, or driveline parts. Both cars were Mustang GT's and I pounded on them for nearly 100,000 miles before I got rid of them. The best thing you can do to keep your car in good shape and reduce wear is to maintain it properly and drive it per the manufacturer's recommendations.
Brakes are cheap but transmissions are made to be shifted, use them both. Oh, and rev matching is cool...