It's absolutely _trivial_ to demonstrate that 1ms is not unconditionally enough.
Take a long pipe with a several ms of delay. Run a single TCP flow across it. Observe that your flow gets nowhere near line rate, but instead it sawtooths against line rate and leaves the link idle for a significant amount of time.
Yes, a single flow is a corner case but not not an outrageous one. The behavior also holds true for a small number of flows, especially if they experience identical end to end delays.