In the article Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark, the authors introduced implementation of phase estimation with two qubits only. The trick that bits representing a phase are found piece by piece. Although, this is at the cost of repeated calculations, in the end the number of qubits saved is material. Moreover, the circuit is much less complex. Both these features seems to me crucial in NISQ era.
I realized that such approach to the phase estimation was exploited in hybrid HHL algorithm (Large-scale quantum hybrid solution for linear systems of equations) and something similar in implementation of QFT in Shor's algorithm (Experimental Study of Shor's Factoring Algorithm on IBM Q).
Although the iterative phase estimation was introduced more than 14 years ago, I did not notice their significant exploitation. Therefore, my question is why this approach is not widely used? Is there any factor that hinders its application?