No - you're mixing the terms "entropy" and "(pseudo)random bits". A CSPRNG can't be a source of entropy, period -- as noted above, it's always a deterministic function of its inputs. Entropy comes from truly unpredictable events, such as thermal noise, radioactive decay or cosmic radiation, etc.
One uses a CSPRNG to generate a sequence of pseudorandom bits, wherein the sequence can only be predicted if the initial input to the CSPRNG is known (the "seed"). If you want a really "random" key, the usual trick is to "harvest" some entropy from the system (e.g., from hardware sources, such as mouse timings, or dedicated hardware random generators based upon things believed to be physically random), condition it (make it uniformly distributed, unbiased, etc.), and then use those harvested "truly random" bits to seed your CSPRNG.
Real, sound cryptosystems routinely --- in fact, almost invariably --- source their keys from CSPRNGs. CSPRNGs can't source entropy, as you say, but in cryptography we're not looking for entropy. We're looking for unpredictability.
What confuses people is that cryptography usually jumpstarts itself with a small amount of entropy (or something close enough to entropy to count). That small seed of entropy gives us unpredictability for the life of the system, even though the bits we actually use will come from deterministic processes.
One uses a CSPRNG to generate a sequence of pseudorandom bits, wherein the sequence can only be predicted if the initial input to the CSPRNG is known (the "seed"). If you want a really "random" key, the usual trick is to "harvest" some entropy from the system (e.g., from hardware sources, such as mouse timings, or dedicated hardware random generators based upon things believed to be physically random), condition it (make it uniformly distributed, unbiased, etc.), and then use those harvested "truly random" bits to seed your CSPRNG.