This law does not apply to queueing as encountered in routers. It assumes unbounded queues and a poisson arrival process (i.e. a memoryless channel); both assumptions don't hold for packet routers and senders using congestion control (TCP or otherwise).

There is, however, a high chance of encountering buffer bloat if countermeasures are not taken at the chokepoint: https://en.wikipedia.org/wiki/Bufferbloat

Modern cable modems, for example, are required to implement such countermeasures. My ISP is at over 90% capacity and round trip times are still mostly reasonable. (Bandwidth is atrocious, of course.)