By no means comprehensive, but a couple of downsides:
First, civilian shipping will only go within your jump gate network at a distance of 4 jumps. Meaning that from whatever planet they're orbiting, it must be max 4 jumps and have gates. So if it's farther away or if you've got it connected with jump tenders, you'll need your own.
Costs money, which is sometimes bad, sometimes doesn't matter.
The infrastructure produced as a trade good by your planets is not accessible to you as the government. This is only important in this context because civilians (should, if things are going right) prioritize your shipping contracts over finding their own work. What that means is that you might have 2,000 infrastructure available on Earth as a trade good, but without civilian freighters to move it, it won't go anywhere. That can be a very useful resource in colonization, particularly in your starting system.
Aside from those, civilian shipping's lovely. I usually have a couple or eight freighter fleets running around, but when I really want to build out a new auto-mine or get a colony over 25 mil colonists, I'll use a round or two of civilian contracts to bolster it.
