I used to do that in my old beetle that had a clutch that was quite weak. I only used the clutch in 1st gear, the rest of the upshifts by ear. There was enough slop in the gears that you could do that all day long and never miss.

Were they timed to make it reasonable to go directly from n to n+1 or did you have to shift to neutral, wait, then upshift?

I have a not-so-old Audi with a known-bad gearbox w/ faulty synchros and because it is a turbo you really can’t upshift in that band when/where the gears are lined up without losing too much power so I have learned to time how long I should wait in neutral (for the RPMs to drop) before completing the upshift. Non-sequential downshifting after slowing down from a higher gear is much harder though - you really have to play it by ear based off the sound/RPMs and the current speed both. And it’s a six speed with considerably less slop than the old Beetles used to have.

The trick is to match the rpms as the engine drops naturally you just slot it in gear at the right moment. If you do it often enough at some point you don't even notice anymore until you try to drive another vehicle, at which point hilarity will ensue.

Those old beetles were just four speeds, pretty beefy gears. I never managed a good downshift though, I would cheat and very briefly depress the clutch so it wouldn't slip. Do it too long and you'd get that horribly expensive smell. I was dirt poor and got the car for free so I really couldn't complain. Baby blue. And it taught me to be very careful on wet surfaces with a rear mounted engine (took out a bicycle stand with it in front of one of the busiest coffee places in Amsterdam West, "Tramlijn Begeerte" (dutch translation of a 'streetcar called desire'). Funny little car.

For the downshifting, you can speed things up if you spin up the input shaft by putting the gear selector in neutral with the clutch engaged (foot off it) and rev the engine to increase the speed of the input shaft, then clutch back in, and select the lower gear (now with the input shaft going faster [as is needed], the synchros have much less work to do to engage the lower gear).

I had an old Alfa Romeo that was fantastic overall but had a pretty terrible transmission, especially when cold. You do learn quickly how to get by. :)

This works for upshifting too, it's known as double clutching.

If you have a turbo diesel it's a good skill to learn as you can shift smoothly while still keeping the turbo spooled up and not cause as much wear on the gearbox.

I do that regularly in all stick shift vehicles (rev matching). It's a lot more challenging without a synchro at all, though!