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).
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.)
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.)