The very slow is the issue. Assuming we can reach 10-20% of c, we can reach a couple of nearby stars in 200 years (Wikipedia gives me 50 stars with 30 ly).

200 years is roughly the time from the Napoleonic era from today (Taking an Euro reference). Do you remember what your ancestor were doing during Napoleon Russian campaign or when US purchased Louisiana?

Society changed massively since Napoleon. Over 200 years the society culture of a generation ship would also drastically diverge from ours. Moreover, I can't think of many piece of technology which can keep working for 200 years without a few massive overall.