What's the advantage of using OFB/CFB/CTR modes over a stream cipher
There is no real advantage, other than the fact that it allows you to convert a block cipher into a stream cipher securely.  Since there has been a large amount of research put into block ciphers and ciphers such as AES are commonly implemented in hardware (such as AES-NI), it allows for reuse of the primitives.

Side note: the nonce generally does not need to be random to be secure, it just needs to be unique.  Since it will be irreversibly and unpredictably permuted by the block cipher it can be predictable unlike an IV, but a nonce reuse is significantly more devastating than an IV reuse.