Yes. The number of $n$-bit blocks you can encrypt with this construction is proportional to $2^n$ instead of just $2^{n/2}$. So for AES this shouldn't be a problem because you can't process anything near $2^{128}$ blocks.

A secure stream cipher can be constructed from a PRF using something similar to AES-CTR.

AES is more accurately described as a PRP than a PRF, but this distinction is unimportant if the number of queries an attacker is allowed to make under a given key is much much less than $2^{64}$.

_{(See PRF switching lemma. If $q$, the number of queries the attacker can make, is much much less than $2^{n/2}$, then it is safe to substitute an $n$-bit PRP for a PRF. This is where AES-CTR's limit comes from.)}

However it has been proven that the XOR of two PRPs is a secure PRF instead for up to $\mathcal{O}(2^n)$ queries. ^{1 2}

Readers should note that this isn't the same as saying that you can use up to precisely $2^n$ blocks. For this reason, I strongly discourage using a block cipher algorithm with smaller blocks (like DES, Simon, or Speck) in this kind of construct. (Or any other mode, I suppose.)

Yes. The number of $n$-bit blocks you can encrypt with this construction is proportional to $2^n$ instead of just $2^{n/2}$. So for AES this shouldn't be a problem because you can't process anything near $2^{128}$ blocks.

A secure stream cipher can be constructed from a PRF using something similar to AES-CTR.

AES is more accurately described as a PRP than a PRF, but this distinction is unimportant if the number of queries an attacker is allowed to make under a given key is much much less than $2^{64}$.

_{(See PRF switching lemma. If the number of queries the attacker can make is much less than $2^{n/2}$, then it is safe to substitute an $n$-bit PRP for a PRF. This is where AES-CTR's limit comes from.)}

However it has been proven that the XOR of two PRPs is a secure PRF instead for up to $\mathcal{O}(2^n)$ queries. ^{1 2}

Readers should note that this isn't the same as saying that you can use up to precisely $2^n$ blocks. For this reason, I strongly discourage using a block cipher algorithm with smaller blocks (like DES, Simon, or Speck) in this kind of construct. (Or any other mode, I suppose.)

Yes. The number of $n$-bit blocks you can encrypt with this construction is proportional to $2^n$ instead of just $2^{n/2}$. So for AES this shouldn't be a problem because you can't process anything near $2^{128}$ blocks.

A secure stream cipher can be constructed from a PRF using something similar to AES-CTR.

AES is more accurately described as a PRP than a PRF, but this distinction is unimportant if the number of queries an attacker is allowed to make under a given key is much much less than $2^{64}$.

_{(See PRF switching lemma. If $q$, the number of queries the attacker can make, is much much less than $2^{n/2}$, then it is safe to substitute an $n$-bit PRP for a PRF. This is where AES-CTR's limit comes from.)}

However it has been proven that the XOR of two PRPs is a secure PRF instead for up to $\mathcal{O}(2^n)$ queries. ^{1 2}

Readers should note that this isn't the same as saying it you can use up to precisely $2^n$. For this reason I strongly discourage using a block cipher algorithm with smaller blocks. (Like DES, Simon, or Speck.)

Yes. The number of $n$-bit blocks you can encrypt with this construction is proportional to $2^n$ instead of just $2^{n/2}$. So for AES this shouldn't be a problem because you can't process anything near $2^{128}$ blocks.

A secure stream cipher can be constructed from a PRF using something similar to AES-CTR.

AES is more accurately described as a PRP than a PRF, but this distinction is unimportant if the number of queries an attacker is allowed to make under a given key is much much less than $2^{64}$.

_{(See PRF switching lemma. If $q$, the number of queries the attacker can make, is much much less than $2^{n/2}$, then it is safe to substitute an $n$-bit PRP for a PRF. This is where AES-CTR's limit comes from.)}

However it has been proven that the XOR of two PRPs is a secure PRF instead for up to $\mathcal{O}(2^n)$ queries. ^{1 2}

Readers should note that this isn't the same as saying that you can use up to precisely $2^n$ blocks. For this reason, I strongly discourage using a block cipher algorithm with smaller blocks (like DES, Simon, or Speck) in this kind of construct. (Or any other mode, I suppose.)