Dice rolls are not the same as generating a seed. With a dice roll there are six possible outcomes, generating a seed, there are many more possible outcomes.
And that's the only difference. If you want to get some 256-bit number, it does not matter if you call some function that will return true/false 256 times, or if you call another function, that will return 256-bit value directly. If you have a state, then you can get it bit-by-bit and execute exactly the same algorithm. For deterministic outputs, you could get exactly the same results if you have a state. For random results, you can still get many samples and check if it is random enough, just by running the same randomness tests.
You also care that a particular outcome does not affect the next outcome, in other words, that each outcome is independent of all other outcomes.
If you have a stateless function, then it is theoretically possible to get {4,4,4,4,4} result, mentioned above. If you have some kind of state, then you can design your algorithm differently, just to pass some randomness tests. And that will make your outputs more random, but also less resistant to some attacks, because then you can assume that you will never get {4,4,4,4,4}, just because that value will fail some randomness tests. Of course, usually the size of the output will protect you from those attacks, and you will not even notice that potential weakness.