What does a stream cipher provide that cannot be obtained with AES CTR mode operation? I can precompute the key stream for the CTR mode operation and the encryption at that point is similar to a stream cipher. So why are there stream ciphers still used and proposed after RC4? Recently the ChaCha20 as part of the ChaCha20-Poly1305 AE cipher.

Are there advantages to using a stream cipher especially?
AES-CTR is a stream cipher, of a particular kind where the keystream is obtained by encryption of a counter. So the question reduces to: what are drawbacks of AES-CTR compared to other stream ciphers?

The main ones compared to ChaCha20 are:


Without hardware support, AES can fail to cache-timing attacks.
Without hardware support, AES is slower.
Without hardware support, the fastest implementations of AES use significant memory.
Pre-computed AES subkeys (which speeds-up things) require not quite negligible memory (160 bytes for AES-128 in addition to the base key, compared to none for ChaCha20); this is an issue when many sessions each with a different key are active simultaneously.
There's a theoretical distinguisher for AES after about $2^{68}$ bytes (but it requires as much memory, and wouldn't be much a practical issue anyway).


Compared to other modern stream ciphers like Trivium, AES requires more hardware at comparable speed. On the other hand it allows random access to the keystream, and parallelization (as ChaCha20 does), when many other stream ciphers (including Trivium and RC4) do not.

Bare AES-CTR does not provide authenticated encryption (AES-GCM does, and uses AES-CTR for encryption), so comparison to ChaCha20-Poly1305 is unfair.