The use of unmanned aerial vehicle (UAV)-based communication in millimeter-wave (mmWave) frequencies to provide on-demand radio access is a promising approach to improve capacity and coverage in beyond-5G (B5G) systems. There are several design aspects to be addressed when optimizing for the deployment of such UAV base stations. As traffic demand of mobile users varies across time and space, dynamic algorithms that correspondingly adjust the UAV locations are essential to maximize performance. In addition to careful tracking of spatio-temporal user/traffic activity, such optimization needs to account for realistic backhaul constraints. In this work, we first review the latest 3GPP activities behind integrated access and backhaul system design, support for UAV base stations, and mmWave radio relaying functionality. We then compare static and mobile UAV-based communication options under practical assumptions on the mmWave system layout, mobility and clusterization of users, antenna array geometry, and dynamic backhauling. We demonstrate that leveraging the UAV mobility to serve moving users may improve the overall system performance even in the presence of backhaul capacity limitations.