At TL 9 a Fire & Movement capital stops being able to build any ships except Adamants unless it is getting chronimium through a trade route. At TL10 all it can build is basic infantry. New players get blindsided by this pretty often. I would suggest that the quantum and post-industrial programs require chronimium to build.

Imperial capitals could also stand to have some special trait or effect to distinguish them from sector capitals, and it should be possible to manually designate a sector capital as the new imperial capital.