I am reading this thread in wonder, because there are some misconceptions.
First, "rev matching" is part of what was called double-clutching or double-declutching (side of the pond dependent). It is also referred to in the context of the "Heel-Toe Technique".
Double-clutching is called "double" from the days of no synchronizers. Heel-Toe is a way to brake and downshift at the same time. To double-clutch, you press the clutch in, "blip" the gas to match the engine revs of the next lower gear, and shift to neutral. Then immediately, you clutch in again, blip the gas to the gear speed, and shift into the lower gear, and then clutch out. With synchronizers, you can skip the clutch in/out to neutral.
First gear is a special case. The gear speed and syncros here are sensitive, so you should double to first to save synchro wear.
Now, with a good tranny and a really good feel, you can skip the clutch part entirely and match the speeds with the throttle. This is the technique used when you hear someone race announcer talking about a driver being a left-foot braker. Look ma, no clutch.
Heel-Toe Techinique is right foot braking with either the toes or the heel on the brake and the reverse on the gas while the left foot is on the clutch. The driver is braking hard and declutching at the same time down through the gears. The advantages are that the driven wheels have the engine to help slow the car (marginally compared to the brakes), the engine helps resist lockup of those wheels (body in motion stuff), the driver has the throttle available to correct issues, and the exit gear is ready as soon as it can be applied.
If you downshift and "drag" the engine up when you declutch, you are wearing the clutch plates out. You may be wearing out the clutch plate almost as much as resting your foot on the clutch, but I cannot swear to that. You also are putting more wear on the synchronizers. If you drag the engine up, you are also giving a lurch to your passengers.
If you use the clutch a lot, you are putting more wear on the throw-out bearing, but sitting idle with the clutch in probably does a lot more wearing.
The reason to declutch and be in the right gear at all times is to save your life. Consider that defensive driving is not about stopping, but being aware of a situation and "driving" out of it. If you are going 20 mph in 4th, you will not have the throttle response on most cars to accelerate out of a situation (degrees of freedom baby.) Although this is generally mute with ABS (there are instances where ABS is not your friend), the engine will help control lockup.
The other reasons are just boy racer pleasure 😉 Going into a turn down through 3 gears from 8 grand in an Integra Type-R gives me that peculiar feeling 😉
Oh, since I said it and someone will want to flame it... ABS is not your friend when wet leaves or sand is on a hard surface and you have to stop. Here is where a little lockup is good because that slippery snot can be plowed through to real pavement. Does not happen often, but some folks driveways are downhill. With the wet fall leaves on your drive way, look out house 😱