Unmanned aerial vehicles (UAVs) have emerged as a promising solution to establish links to reach edge servers (ESs) in scenarios where ground users (GUs) lack direct connections. However, a predominant focus in existing research on UAV deployment centers around optimizing system performance under the consideration of a fixed computing resource pool, resulting in a potential computing bottleneck for delivering largescale multi-access edge computing (MEC) services. In this article, we present an innovative approach, aiming at enhancing MEC performance by expanding the computing resource pool in a UAV-assisted system through effective management of UAV altitude and mobility. With this idea, the joint design of communications and computing needs to be reconsidered. Specifically, we briefly overview the problems when leveraging UAVs to coordinate communication and computing resources, and review closely related work on UAV-assisted MEC systems. Then, we elaborate on the proposed service network architecture, the modeling, and related optimization problems to boost the utilization of resources. Finally, we utilize a use case to demonstrate the effectiveness of our design approach and point out several research directions.