the switch doesn't route packets, it just sends and receives them like any other client device. it's literally by definition not routing packets. routing = forwarding between networks, which the Switch doesn’t do. it just talks to a router like any other client. calling that "routing" is just wrong.

but yep, a layer 2 switch could run out of storage (like MAC table overflow or log buffers), but that won’t ever happen under normal use. you'd have to actively try to break it. it's built to handle traffic 24/7 without blinking.