I still do sometimes, just to keep the skills up. Like a pilot who still uses VOR navaids even though his glass panel has a perfectly good GPS in it. Never know when I’ll end up driving some old beast that requires the technique.
I got into the habit of double clutching to downshift many years ago driving a pickup truck on steep gravel roads, and so as a force of habit I do it whenever I downshift to slow down, usually that is from 5th or 4th to 3rd, without even thinking about it. In 40 years of driving manual transmission vehicles I’ve never had to replace a clutch, including the throw-out bearing. My current car has over 200K on the same clutch. Knock on wood … lol …
As far as syncos, I’ve always thought syncro damage was caused more by aggressive up shifting, you know where you really want to accelerate fast from 0 to 60 mph so you slam the shifter into place gear to gear with very little transition time. Double clutching isn’t for that problem, it’s primarily for when you downshift to slow down. Double clutching if done properly matches the rpm of the clutch disk to the flywheel better, and does reduce wear and heat glazing on the clutch disc and flywheel surface. It also helps to make the speed reduction feel more smooth and in control. It’s true that there’s more throw out bearing wear and tear, that’s a downside.
With smaller light weight cars these days I doubt there’s any wear and tear reason to double clutch besides the smoother feel it provides. For heavier vehicles I imagine it could lengthen the miles between clutch replacements somewhat. If you really want to minimize wear and tear expense you’re probably better to just use the brakes to slow down. There will be more brake jobs needed, but brake parts are designed to be easily and relatively inexpensive to service and replace.
I am also a victim of my first throttle-by-wire. It’s inconsistency makes rev-matching a matter of luck instead of skill. I also gave-up and just shift. I’m afraid this “feature” will hasten the demise of M/T vehicles.
Assuming you mean double-clutching on downshifts. I “double clutch” when I rev-match downshifts. Just how I learned. I can do it with the clutch held in too. I asked a guy I went to engineering school with who later became a race car driver about it and he had a day’s long explanation about why he does it in certain circumstances. Want to watch him do it? Here. He double-clutches on the second overall shift in the video, which is the first downshift. I had a 2007 perfect Miata that someone I loaned it to “ruined” with improper shifts. The person rounded off the synchros on a rushed down shift.I ended up trading it for mostly that reason. Almost every automaker now has rev-matching software that does it perfectly every time. It was first on the 370Z, but it is common now. I’ve driven it on track at media events in a 370Z and Corvette and it makes you feel like a hero. And if you are a purist, you can turn it off. In the "Vette, the paddle shifters actually are the on-off switch if I remember correctly.