Why is the whole initial state used in the final addition of Salsa20 and ChaCha?
Note that, in Salsa20, the loads and additions of the key words ($x_1$, $x_2$, $x_3$,
  $x_4$, $x_{11}$, $x_{12}$, $x_{13}$, $x_{14}$) are critical for security, since the double-round function is
  trivially invertible. One might think that the remaining loads and additions could
  be skipped without sacrificing security, achieving almost half of the HSalsa20
  savings. However, this change would interfere with the vector loads and vector
  additions used in many high-speed Salsa20 implementations.


from D. J. Bernstein - Extending the Salsa20 nonce

Since you need to supply the nonce/counter to pass them to the next block, you need to keep track of them anyways, eliminating the space savings.