Because the booster might cost something like $20 million and the fuel cost is like $200,000 per launch. The fuel cost is 1% of the cost. If you can recover the booster and re-use it 10 times or more (without all the refurbishment required for each turn of the Space Shuttle), you've reduced launch cost considerably. If you can do this, it might make sense to just build a bigger re-usable booster, if you need to launch more mass.
SpaceX is doing this the right way: They want to test re-use; so, they increased the fuel capacity and upgraded the engines. There was no lose of up-mass, in fact it increased. Having done this, they still have the margin to bring the booster back. NASA never tried this for three reasons: (1) Every launch is basically a one-off, unique mission. Standardization was driven by Air Force and commercial interests. (2) Their budget is so tight that, if they could save a couple million on a given mission by using a throw away booster, they would. They put onerous flight rules in place, which guaranteed the cost of recertification of the vehicle for re-use made it uneconomical. (SpaceX is contractually obligated to use a new booster and new cargo/crew module for each ISS mission, even though they are theoretically re-usable -- they plan to re-use some of the components for commercial flights) (3)They convinced themselves it couldn't be done. They assumed the booster couldn't be controlled on re-entry -- it would tumble. They convinced themselves that firing an engine into a supersonic flow (engine pointed in the direction of travel, to slow the vehicle) would not be stable and would not allow for precision control of the vehicle.