Turbo lag on a modern engine is minimal such that if you're experiencing it you"re not driving properly. If you're in too high a gear you'll get lag, if you're in the right gear then lag is negligible. Turbocharged engines are far more efficient as they're utilising energy that would otherwise be wasted.
Modern cars are less leggy cause the use smaller turbos. This is possible due to modern electronic engine management systems that enable the use of turbos with higher compression ratio engines while the engine management system can control knock (exploding air/fuel mix rather than burning air/fuel mix). Even later development is direct injection, a technology that suddenly pulled Diesel engines out of the Stone Age, is now starting to be introduced which will further enable lag to be defeated. Back in the '80's when engine management systems were quite basic you had to reduce the engines compression ratio to avoid knock meaning larger turbos to increase the flow rate, which meant very leggy turbos.
Also turbos generate more torque, and it is torque that is more important as it means you can push bigger gears, hence better efficiency and acceleration.
The anti lag mechanisms work in various ways, but the best is the variable vane set up which is better than a complicated, heavy and expensive twin sequential turbo set up. Other methods include introducing fuel into the exhaust manifold which is burned to increase exhaust manifold pressure, but clearly this requires some pretty advanced materials in both the turbos and the exhaust manifold to handle the high temperatures and is prohibitively expensive for normal road cars.
Contrary to popular belief a turbo does not act like a windmill. You're not trying to 'blow' gas through it as high speed. Turbos use the expansion of a hot gas to extract the heat energy out of the exhaust gas. The hot exhaust gas is at a high temperature and pressure at the turbo inlet with a very slow speed -almost zero. The hot gas then expands as it passes through the turbo and cools as it does so. It is the expansion and acceleration of the gas from almost zero to a very high velocity as it expands that drives the turbo. So minimising turbo lag is not not about 'keeping the turbo spinning', it's about maintaining gas pressure and temperature in the exhaust manifold.
I suspect the F1 cars will be using direct injection engines with variable vane turbos and some form of fuel injection into the exhaust manifold - but they're less concerned about lag as they are keeping the engine speed high which maintains exhaust gas flow which in turn maintains exhaust gas pressure.
So in answer to the original question, turbos are a very elegant solution. Normally aspirated is just inefficient and superchargers are plain stupid as they take more energy out of the engine rather than utilising energy that would otherwise be wasted, thus further reducing efficiency.