Well it's the opposite of what everyone is saying IMO. When you press in the clutch and start playing with your gears without having shifted to neutral and letting the clutch out (double clutching) you have not slowed your shaft speed. You are asking the synchros, the most vulnerable part of the trans to do work.
So while you think you are saving your transmission by not rowing down through your gears one by one, you are actually wearing it out more. What is vulnerable here is the clutch, and the clutch wears very very little when you rev match. If you don't rev match, that's a different story. If you are going to coast and go through your gears, you should go to neutral, let off the clutch, reduce shaft speed, then hold the clutch back in and row through. The key is always during that double clutch, where you've let the clutch out in neutral, you've reduced shaft speed.
As far as engine wear... A few revolutions extra until you come to a stop is meaningless. But... I can tell you for sure as I enquired with a major race engine builder here... You are greatly REDUCING operating temps when coasting in gear. What's happening is that your cooling system... Water pump, oil coolers, etc are still working at speed. While there is no longer any high pressure combustion inside the cylinders that normally causes heat. So a rapid cooling effect takes place, heat is quickly scavenged out, and that is better for the motor than any "wear" taking place because your RPM'S are a bit higher for the next 10 seconds, until you come to a stop. The reduced brake wear is a bonus.
and it puts a smile on my face every time. It will be infinitely more glorious once I get my test pipe in.
