Wireless mesh networks play a critical role in enabling key networking scenarios in beyond-5G (B5G) and 6G networks, including integrated access and backhaul (IAB), multi-hop sidelinks, and V2X. However, it still poses a challenge to deliver scalable per-node throughput via mesh networking, which significantly limits the potential of large-scale deployment of wireless mesh networks. Existing research has achieved $O(1)$ per-node throughput in a dense network, but how to achieve scalability remains an unresolved issue for an extended wireless network where the network size increases with a constant node density. This issue prevents a wireless mesh network from large-scale deployment. To this end, this paper aims to develop a theoretical approach to achieving scalable per-node throughput in wireless mesh networks. First, the key factors that limit the per-node throughput of wireless mesh networks are analyzed, through which two major ones are identified, i.e., link sharing and interference. Next, a multi-tier hierarchical architecture is proposed to overcome the link-sharing issue. The inter-tier interference under this architecture is then mitigated by utilizing orthogonal frequency allocation between adjacent tiers, while the intra-tier interference is reduced by considering two specific transmission schemes, one is MIMO spatial multiplexing with time-division, the other is MIMO beamforming. Theoretical analysis shows that the multi-tier mesh networking architecture can achieve a per-node throughput of $Θ(1)$ in both schemes, as long as certain conditions on network parameters including bandwidth, antenna numbers, and node numbers of each tier are satisfied. A case study on a realistic deployment of 10,000 nodes is then carried out, which demonstrates that a scalable throughput of $Θ(1)$ is achievable with a reasonable assumption on bandwidth and antenna numbers.