It's a cool idea, but the reality is centuries away. Three points to consider:
1 - Useful spacecraft are generally bleeding-edge technology, with lots of ways for tiny faults put them out of action. We're not talking wooden rowboats here.
2 - The number of deep-mastery experts needed to build a spacecraft "from scratch" is huge. Talk to someone who's even vaguely familiar with the staffing requirements for a modern chip fab, and its whole supply chain.
3 - As technology advances, the number of experts in point #2 keeps growing. And the self-replicating spacecraft will, in effect, need all of their smarts "built in".