You can easily predict the output of a system from its input, if said input can only take a few possible values, by simply trying all possible inputs until you find one which matches the output. The extra step of hashing the pool into a key to a keystream generator does not prevent that. If the key has only a few possible values, and you can observe enough of its output, you can brute force it.

If, for instance, the pool has only 256 possible values (8 bits of entropy), perhaps because the system just booted and almost nothing has been added yet to the pool, there will be only 256 possible keys, and only 256 possible output streams. If you have enough of the output (on average around one byte), you can try the 256 possible pool states, and see which one would give you the same output you have. And since now you know both the pool and generator state, the system's entropy is now zero: it's completely predictable.

The only way to prevent that is to never output anything, until the number of possible states is large enough (like 2^128 or more) that brute forcing is not viable. Which AFAIK is what the new getrandom() syscall does.