Everything you bring to space has weight.
Weight which you need to push along with fuel.
If your fuel tanks are empty there is no reason to Carry that weight around and let your remaining precious fuel be wasted faster. **You are still pushing the whole rocket with less and less fuel.**
**So we throw the spent parts of a rocket off.**
That is btw why space x sometimes wont recover boosters. If you wanna get deeper into space you wont carry enough fuel to save those spent parts.. as saving the rocket parts needs more fuel. and why the standard was to waste rockets entirely because… u can get farther.
Not to mention saving boosters is just difficult in the first place
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