Great question.
As said early, lighter cars have an edge. Even if it is down on power compared to the other lane.
Removing weight from the car doesn't make the car less reliable, but more dangerous. If you start replacing doors with fiberglass, this is now a drive at your own risk for fear of lifeand/or limb. Street or track.
Things like bumpers, hood and deck lids are the norm. for lightening with fenders seen alot as weight reduction items. The cost can be reduced through resale of the replaced parts. This makes it a good spot to spend money. Paint optional cost of course.
With the lighter weight, getting off the line is easier and motoring on down the track is easier and quicker with the best bennifit yet, less strain on the engine/drivetrain. Since your engine is working less/not as hard I should say really, in order to move the weight, it shouldn't get so beat up....so to speak.
From my veiw, adding the like cost to the engine is the flip side of the coin with it's own cave eats. While the cars body is still strong and better in case of a fender bender, it'll still need to be stiffened for the increased power. Something a fiberglass car should do anyway.
Adding power to the engine in normal cases tends to move the power band up through cams, intakes, carb sizes etc.... and creates a harder running/charging engine. You still have the weight to overcome. Enter a higher stall converter and axle ratio.
The great equalizer to adding bigger cams and the like for more power would be to super charge the engine. RPM power curve stays the same. It just moves up alot in power while the RPM curve doesn't really change much.
At, oh, lets say, a $3500 cost for a enterly level Paxton and about a days work on the car, you can increase the power by 100 HP and lbs. of torque. For a street car to lose the equal amount of weight to power gained vs the Charger, it may be difficult to balance out. Once you move beyond a basic improved muscle car power upgrade to something considered radical (By the ave. guy walking around) you'll probably find most people went the engine route rather than weight savings.
In reality your best bang often comes from a combination if weight reduction and power upgrades.
AS dually noted here, how true it is!