Only thing i dont like about a supercharger is it takes power to turn it from the engine. Also as it compresses the air, it becomes hotter. But no lag from a supercharger is awesome. Great for playing around. As mentioned there are ways to spool up a turbo before launching. 2 step, spray it etc.
An intercooler can help that but intercooled turbo inlet temps will be cooler than roots or twin screw supercharger inlet temps imo. Although spraying a small shot of nitrous before the blower will cool inlet temps A LOT,
And all of that adds weight and can mean a difference, more difficult class to race. Nitrous and forced induction are both power adders