When I started biking there were loads of new ideas floating around; Wankel, turbo, inline sixes,even a diesel. You could buy a turbo and bolt it on to your 4cyl Jap with the inevitable consequences to your unmodified engine internals, but the big 4 over come that by making their own versions. Lag was an issue but nowadays that can almost be eliminated so why no turbo bikes? Norton revised the rotary a few years ago to some good effect but it doesn't seem to have caught on. I believe Enfild India made the first (and last) diesel but with modern diesels and turbos I should think it could be made to work.
How about a 2 stroke turbo? Imagine a quarter mile on that!

Kwak make the supercharged H2, but you're right, no turbos.

I've often thought that they could make smaller capacity bikes with turbos rather than the litre bikes. I guess it's a combination of cost and issues with lag and boost, but you'd think with modern tech they could sort it. With emissions regs tightening all the time they just keep increasing engine capacity to replace the power lost by the mapping for emissions. A turbo could help in this situation, but it's telling that Kwak chose the more predictable power delivery of a supercharger.

Also thought about diesel bikes too. Just imagine the fuel economy..... 100mpg+? I suspect that for the most part in the west, bikes are less essential transport and more weekend fun.. So a diesel would have a limited market. And why go to the expense of a turbo, when many bikers don't care about fuel economy so carry on making bigger and bigger engines. Just my thoughts...

Just recently joined the cliché and bought a BMW r1200gs.

Ps. Just to add.... Electric motorbikes are improving so they could be another avenue to explore. They haven't really taken off yet though. Whereas electric pedal bikes are everywhere. Saw a guy (bellend) riding his modded ebike at about 40mph up our road. No helmet and obviously completely illegal. Must admit it looked like immense fun!!

I'd forgotten E bikes, TBH I've only seen little chinese ones which didn't seem like 'real' bikes, no doubt once the big 4 start producing them things will change.

Zero make some good looking ones

https://www.zeromotorcycles.com/en-gb

I have a feeling that it's not possible to turbocharge a two-stroke. Something to do with the exhaust needing to be perfectly tuned to create the scavenging effect

I understand it's done on snow mobiles but is not without it's problems.

There used to be turbocharged 2 stroke diesel trucks a while ago.

Found a clip on YouTube

I think Commer did them in the UK

I think the issue is that turbocharging works for a big 2-stroke diesel, but not so well for small petrol/gas engines.