A turbocharger isn't a fan. The amount of power it takes to spin is actually incredible. That's why "Electric turbos" were a classic scam until the past decade

A turbocharger isn't a fan. The amount of power it takes to spin is actually incredible. That's why "Electric turbos" were a classic scam until the past decade or so, when they are an extremely weird product that still isn't very good. Like, producing 1 bar of boost for a 2L engine is somewhere between 30-70 hp! Turbos extract that energy from otherwise wasted, extremely hot exhaust gases, which is what makes them efficient. That's also what made them an improvement over supercharging for the majority of applications, because in a supercharger that energy cost comes direct from your usable power. What "fixed" turbolag in any engine that isn't an 8L diesel is things like variable geometry, lightweight turbines, better bearings, better engine management, and just smaller turbos for the same boost. It's also massively impacted by driving behavior. My GTI with a teensy tiny turbo still has a half second or so of lag if you try to go from no throttle to full throttle, like if you are really bad at "launching", but if you know what you are doing you will be holding some revs such that the ECU can slap open the throttle plate and dump fuel in just a few cycles and get full 1 bar of boost by the time your clutch is fully engaged. I have done this accidentally more times than I would like to admit, which tends to spin the tires :/ Formula 1 adopted the exact system you are describing, but it's stupid expensive for minimal benefit and I would bet is used more for energy recovery from waste exhaust gasses than actual lag reduction, since F1 cars should be able to almost never be in a regime that would result in lag, and if you have spare joules, you can just throw them directly at the wheels instead of the turbo. It's called the MGU-H system.