Does cryptographically-secure pseudo random generators require a secure seed? For any cryptographically-secure pseudo random generators, do we need a secure random seed for those?
If the seed is predictable, then everything is broken due to the deterministic propetry of the algorithms.
Actually, your second sentence itself is the answer. A pseudo random number generator(cryptographically secure or not) is a deterministic algorithm which produce random looking numbers. Every time you provide the same seed it produces the same random looking numbers. Now, if your seed value is predictable and algorithm is public then the output of the deterministic algorithm is also predictable. So, the seed of a cryptographically secure pseudo random number generator must be secret, so that the output you get is unpredictable.