Something I've been wondering recently is why a lot of professional motorsports (well, at least rally), when there is a need for an engine to make power, and make it early in the power band, the answer is either a twin-turbo setup, or a turbo with anti-lag. What I don't understand though, is that a supercharger gives the engine low-end torque by itself without needing anti-lag, and an anti-lag system greatly increases wear on the turbo. When you are already pushing the engine hard by the very fact that you are racing, I don't see why you would want to go with a system known to cause additional wear to the engine as a whole, when you could install a part that does the same job by itself, without the need of a second system. I think drag racing is the only area of motorsports that pretty much always goes with superchargers once to get to the professional teams.
Good question. Here is an example. I have a Honda 1.8 engine. Say I want to run a turbo charger that's large enough to put down 600 whp. The size turbo I'd need to move that air is large and will take time to spin, depending on compression and manifold this particular case starts making boost around 4500 and spools completely by around 5k. Now from 5k to 9k rpm I'm a rocket but below I'm not going anywhere. If I use a supercharger on the intake side u can use a small one that will respond immediately, make great power down as low as 2k rpm and as the supercharger chokes out at 5k, it gets bypassed to leave the turbo to do its job. It's a complex system, but it gives you the chance of making big torque way down low with a small engine that normally would make most of its torque way up top. It's very versatile once you get it right. I would only do that for a road race setup. Torque doesn't make a difference if your launching your 600hp big turbo engine at 6500rpm anyway and brake boosting. The main benefit to twin charging is you can usually get a larger power band than only one or the other. Also, anti lag is very hard on the turbo itself. You won't see many anti lag setups on the street, but it's not hard to make 400whp on a 1.8 and avoid the worst of the lag. It's the 600 and up club that struggle.
Simply put, the engine requires more air at higher rpms than the blower can produce (to maintain desired boost that is). While a turbo can spin waaay faster than the motor once spooled (especially since more boost=more exhaust gas=more pressure to spin the turbo), a blower will always spin at the same ratio of crank speed regardless of the amount of air required or the amount of boost being produced (ignoring belt slip and centripital superchargers). Superchargers also create more load on a motor than turbos, and this parasitic loss becomes more of an issue as the engine requires more and more air. Thats not to say that they don't work above a certain rpm, but they do lack the ability to scale output at the same rate that the engine requires it. Disengaging the blower at high rpms is still more detrimental than just letting it do its thing, unless you have a turbo to pick up where it left off.
To combat the supercharger choking out I had thought up a cool idea a few years back that would use a CVT driveline (like one in a snowmobile or an ATV) that would be electronically controlled like the one on the Honda Rincon (I think that's one of them anyways... they are probably all like that nowadays though) to very the RPM of the supercharger from the crank pulley. This way, you could slowly increase the ratio as the engine revs higher so that the supercharger would then be able to keep up with the engines demand for boost. At the same time, you could make the belt go slack (like an ATV or Snowmobile at idle) and totally disengage the supercharger for things like highway driving or just driving around in heavy traffic. I thought it was a great idea, then I found out that there was a company that actually went and had just patented just a system... I was to slow This thing here is what I am on about, https://www.procharger.com/procharger-i1