In this work, we report on the advantageous aspects of the i-TED Compton imager for proton-range monitoring, based on the results of the first Monte Carlo study of its applicability to this field. i-TED is an array of Compton cameras, that have been designed for neutron-capture nuclear physics experiments, which are characterized by $\gamma$-ray energies spanning up to 5-6 MeV, rather low $\gamma$-ray emission yields and intense neutron induced $\gamma$-ray backgrounds. Our developments to cope with these three aspects are concomitant with those required in the field of hadron therapy, especially in terms of high efficiency for real-time monitoring, low sensitivity to neutron backgrounds and reliable performance at the high $\gamma$-ray energies. We find that signal-to-background ratios can be appreciably improved with i-TED thanks to its light-weight design and the low neutron-capture cross sections of its LaCl$_{3}$ crystals, when compared to other similar systems based on LYSO, CdZnTe or LaBr$_{3}$. Its high time-resolution (CRT$\sim$500 ps) represents an additional advantage for background suppression when operated in pulsed HT mode. Each i-TED module features two detection planes of very large LaCl$_{3}$ monolithic crystals, thereby achieving a high efficiency in coincidence of 0.2% for a point-like 1MeV $\gamma$-ray source at 5 cm distance. This leads to sufficient statistics for reliable image reconstruction with an array of four i-TED detectors assuming clinical intensities of 10$^{8}$ protons per treatment point. The use of a two-plane design instead of three-planes has been preferred owing to the higher attainable efficiency for double time-coincidences than for threefold events. The loss of full-energy events for high energy $\gamma$-rays is compensated by means of Machine-Learning algorithms, which allow one to enhance the signal-to-total ratio up to a factor of 2., Comment: 19 pages, 14 figures. Accepted in Scientific Reports (Submitted: June 2021, Accepted: January 2022)