While your question seems to be focusing on the CTR side of things, its worth an answer to discuss the AES side of things as well.
There are at least two situations where other block ciphers may be more appropriate.
Secure Computation:
There are two main "difficulties" of AES with respect to secure computation (meaning multi-party computation and NIZKs mainly, but also likely fully-homomorphic encryption).
AES is computed over a field of characteristic 2. If an MPC/FHE system uses characteristic $p$ arithmetic, the having a cipher in characteristic 2 requires conversions between different representations (say, of an element in $\mathbb{Z}/p\mathbb{Z}$, or the base-2 decomposition of such an element) which are more costly than in standard computation.
Generically, multiplications are much more costly (relatively) than additions in the context of secure computation. This means that one can have a different "cost model" to build ciphers for, where one is more interested in reducing the number of multiplications in the cipher generically.
A cipher to look at for this topic is MiMC (although there was recently a partial attack against this cipher in a "$\mathbb{F}_{2^k}$ version" of it.
It also has "$\mathbb{F}_p$" versions, which are not hit by the attack).
Embedded Systems:
On standard machines, the hardware implementation of AES (via the AES-NI instruction) gives something like a ~40x speedup over optimized software implementations of AES.
This makes it difficult to be competitive with AES when comparing AES-NI to software implementations of other ciphers.
But when you don't have AES-NI, other ciphers can be more competitive.
This post by Matthew Green discusses using alternative to AES (his recommendation when writing this ~8 years ago was not do this, for the record) discusses certain ciphers like Salsa20 offering a 2x - 3x speedup over AES in software.
Note that Salsa20 is technically a stream cipher compared to AES being a block cipher, but this is just to motivate being able to "beat" AES on speed when you don't have access to AES-NI.
A better source for faster ciphers in constrained computing environments is the ongoing NIST Lightweight Cryptography Standardization.
I have not been following this closely, but there is currently much research interest in finding a new cipher to standardize for (essentially) use in embedded systems.
They are currently planning to post their round 3 finalists this upcoming December, so it would not surprise me if within the next few years there was a "new cipher" which replaces the use of AES in embedded systems.