With construction ships being so cheap, any added capability is just going to lead to massive spam. I wouldn't want to make construction ships expensive in raw materials, as it would severely slow down the early game. I think you can make a case though for having a limited empire capacity for construction ships (either through fleet cap, or some other mechanism similar to starbase cap), and that way you can make them more powerful, to be used in a targeted way depending on your priorities. Powers could include things like orbiting a colony to give it faster build speed, or repairing ships where an upgraded starbase isn't present, salvaging debris for resources (as opposed to science ships salvaging for tech), granting some speedup on megastructure building with diminishing returns, and so on.
If you did this though, I think you'd want to take some of the most menial jobs away from them (such as building basic mining/research stations - honestly, past a certain stage of the game this could just be something your starbases are capable of doing in their system), so that you don't need to keep microing them between these tasks and the more interesting roles.