It's not quite that bad. Have you heard of fission-fragment rockets? Highly feasible, and travel times to Alpha Centauri on the order of decades, not millennia. Baffles me that no one talks about them.
They are extremely different. One is a highly impractical idea from the 1940s, and the other is a relatively recent and promising design that continues to be refined.
What's exactly impractical about a nuclear pulse drive - conventionally launched and activated outside the atmosphere? We know how to build that stuff safely to account for launch failures, it has been done with RTGs many times already.
https://en.wikipedia.org/wiki/Fission-fragment_rocket