On the other hand, if you assume that strong AI can exist in a package at least as small as the human brain but without only a dependence on electricity instead of all the physical constraints mentioned above, your spacecraft could look much much smaller. If you give such a civilization 1000 years to iterate on the technology (an insignificant amount of time compared to the timescales involved in evolution), there's no good reason to think they wouldn't be able to shrink the computing technology (and therefore spacecraft technology) by several orders of magnitude. Consider the size difference and computing capacities of our earliest computers and smartwatches today--and we did that in less than 100 years.
The benefits are pretty obvious: it would require vastly fewer resources to travel to other stars, and any intelligence on board the spacecraft would be immortal (plus if it got "bored" on the way, it could power itself down and schedule itself to start up again once it got to where it was going). The stars seem out of reach to us because of the limitations of our lifespans and our bodies, but they would be entirely within the reach of AI. And from the perspective of conserving resources, there would be no reason to send something anywhere near the size of a human being.