Exotic? Hm, back to aluminum bodywork
, eh? 
No, i have no problem with lightweight technology. But things like the clutch, there is no need for them to be carbon fibre - it is a part the size of a fist, gets used a handful of times before expiring, and costs £10k just to manufacture. Over the season i'd guess that a team could easily spend £300k+ on clutches alone, and what the hell is the need for that?? Another example, when McLaren made their Octopus exhaust, they had to use some INSANELY expensive material (i forget the name) for heat shielding. Again, utterly needless in the grand scheme of things - and those parts never even raced!
But it really is a tough one to implement, because the line of what is necessary (depending on your viewpoint) is somewhat blurred. Is F1 an appropriate test bed for advanced materials research? In some cases yes, but in others, i don't see how (such as the aforementioned McLaren exhausts). In other words some material research becomes very useful in the grand scheme, some just a money pit. But it should be addressed at least on some level, in my view.
Aerodynamics is the worst offender though. I dread to think how much has been spent on double DRS systems (just for a handful of races), f-ducts and what have you.