I think that's pretty much it, the whole reason sophisticated CSPRNGs have entropy pools and stuff.
"my understanding is that all stream ciphers leak some bits of the key with enough output"
This is a false statement.
Nowadays, the most frequently used encryption method is to use a stream cipher (more precisely a binary additive synchronous stream cipher), where the automaton that generates the encryption mask stream is implemented with a counter and with an output function that is an unpredictable pseudorandom function, usually either AES or ChaCha20.
With an appropriate pseudorandom function, such a stream cipher does not leak any bits of the key, even with enough output. There are methods of breaking a cipher with enough computation and memory, but those are specific to the pseudorandom function that happens to be used and they are not limited to stream ciphers, they are equally applicable to block ciphers that use the same pseudorandom function. Moreover, the known methods used to construct block ciphers are usually easier to break than good stream ciphers that use the same pseudorandom function.
It is obvious that when you have written "all stream ciphers", what you had in mind were not "all" such ciphers, but certain stream ciphers with very low implementation cost, but also with inadequate strength, which have been specified in many older communication protocols, e.g. in those for mobile phones (because the communication equipment manufacturers only cared about a low production cost, not about security, and the so-called encryption was only added to fool the customers, not to prevent professional attacks). Such cheap stream ciphers have been easily broken by anyone who has studied them seriously.
The ciphers that you have designated by "all stream ciphers" are an extremely small fraction of what is meant by "all stream ciphers" in the cryptographic literature, as I have explained in my previous post.
But doesn't this constitute leakage of the algorithm's internal state in the output? (Albeit, very slow.)
and they are not limited to stream ciphers
I never said any of the above was limited to stream ciphers.
This strikes me as a non-sequitur? Could you provide me with a quote where I misunderstood the term "stream cipher" and how I misunderstood it?
There is a huge number of stream ciphers that have never been broken.
I understand this to mean, that the full version of the algorithm doesn't have any feasible attacks. That the difficulty of the known attacks is so high, there is virtually zero value to them over using brute force.
Based on how the encryption mask stream is generated, there are many kinds of stream ciphers
If you read the thread carefully enough, you can deduce which kind of stream cipher I was thinking of.