The primary reason we are fixated on faster-than-light travel, is because our lifespans are so tiny compared to the travel time to other stars.
This speaks more to our organic limitations than it does for the necessity of FTL travel.
An AI would have no issue taking 10,000 years to go to neighboring stars, nor 10 million years to "colonize" the entire galaxy.
I think the major limitation in our imagination about space travel is that organic beings will be the primary entities traveling the stars.
But seriously, limiting ourselves to light speed here is somewhat... disappointing.
If the speed of light really is something that can't be worked around with warp drives, etc., then who cares if there are aliens or not. They will never be interacted with in any meaningful way, except for maybe the hyper-rich folks on those generation ships.