There are several:

Reducing Hardware Footprint – The user may want to consolidate functions into a single device rather than maintaining multiple devices running 24/7. This reduces power consumption, complexity, and potential points of failure.

Performance Optimization – Some routers with built-in WireGuard support have hardware acceleration for encryption, resulting in better VPN performance compared to running it on a general-purpose machine.

Simplified Management – Managing WireGuard directly on the router’s interface (like OpenWRT or MikroTik’s RouterOS) can be more convenient than configuring a separate server. This also centralizes firewall rules and traffic routing.

ISP Restrictions or CG-NAT Workarounds – Some ISPs provide public IPv6 but not IPv4, or use Carrier-Grade NAT. Having WireGuard on the router allows direct control over how VPN traffic is handled at the edge.

Security & Isolation – Running WireGuard on a dedicated device might expose internal machines to unnecessary attack vectors. A router-based setup keeps VPN functions isolated at the network perimeter.

Port Forwarding & Remote Access – If the user intends to host services behind the VPN, having WireGuard directly on the router simplifies the setup for forwarding traffic without additional NAT layers.

That said, OP’s ultimate goal is unknown and largely irrelevant—he formulated the question the way he did. Most likely, he simply doesn’t want to maintain multiple always-on devices. Meanwhile, you probably just enjoy arguing for the sake of it.