"Travelling at 1% C, such a ship could cross our galaxy in 100,000 years. With pauses for stops, say 1 million years. So in one or two million years a wave of human colonisation could occupy essentially every single habitable world in our galaxy (what a horrible thought!).

Of course, the above makes major assumptions about technology!"

I would say bigger assumptions of human behavior. Why after the first say 500 years, wouldn't our human colonist be more interested in visiting their roots. Or get into a fight with other colonists- "That's our star system". "No, we are supposed to colonized that system- that's the plan from Sol". "Who cares about Sol, we are the ones doing all the work, and you are behind schedule; we are ready and want it." Etc.