Except actual routers don't handle the traffic on the CPU, they have dedicated hardware to actually handle the packets. The CPU basically runs the OS, configures the hardware router, and does housekeeping tasks (e.g. ARP or FDB expirations, NAT cleanup, etc). The only packets that ever reach it are "trap to CPU" situations that don't require acceleration as those are rare or expensive to implement in hardware (e.g. better suited to a CPU). Those usually include management protocols (ICMP, ARP, NDP, STP, etc) or packets with unknown destination (e.g. the first packet to an IP that requires ARP resolution).

That's how you can have multi-Gbps on a router with a 200MHz MIPS CPU. Or Tbps on a router with a quad-core Xeon.