Saving your gearbox is a key aim of this technique.

When you use a manual gearbox without double declutching (or at least 'blipping' on downshifts) you are basically asking the synchromesh to assist in bringing the engine speed up or down to match what is needed for the gear selected. As I have said before, if you didn't have synchro you wouldn't be able to select the gear at all, or if you managed to do it you'd get an almighty crunch.

Synchro makes life easy for the lazy driver. The less lazy can simply blip the throttle and match revs (better than nothing), or you can go a step further and actually dip the clutch, move the gearbox into neutral, then raise (or lower) the revs as needed (ie to 'match revs'), dip the cluch again and finally select the next gear. Basically double the declutch actions, hence the name, to allow a really smooth, exact gearchange. This is how non-synchro cars were (or should have been) driven. Most single-seater racing cars still are non-synchro because it saves weight. Very cool. Very precise. Very much better for the gearbox when under stress.

If you aren't doing it at least on the racetrack you simply don't care about your driving or your car. Go and buy an automatic refrigerator and stop reading about cars.