Is the quality of a PRNG's distribution ideally the same for all seeds?

Putting cryptographic standards of quality aside (difficulty in predicting previous and next outputs from a current one, etc.), and focusing more on e.g. testing and games where randomness makes things exhaustive or fun, so repetitions or similarity of outputs are not desirable.

For a function random(s) which is an ideal-quality PRNG (real PRNGs may be poor) that produces a set of outputs, is random(1), random(2) etc. hypothetically as equally useful as random(H) where H comes from some hardware generated randomness like /dev/random?

My intuition says that it ought to be, and this would be why using the system clock is often just a convenient way to get a different number on separate runs without needing to store it.