There's nothing wrong with the AI designs if you build a large empire. Hell, there's nothing wrong with them even if you just take it kind of slow.
I'm not saying you don't get big advantages by designing your own ships--because you do--but the AI-designed spaceports are not bad at all. You can build small ones all over your empire at reasonable cost, pepper middle-sized ones around evenly to help reduce the load, and only build your large ones at worlds where you need a strong ship-building presence, or ones that need that extra bit of defense (although to be honest, Defensive Bases are better for that).
If you have a small 4-slot spaceport at every world, and medium ones (with 8 slots, I think?) peppered about, and those nice 15-slot Large ones at your critical worlds, you won't have any problem producing ships at all unless you try to build them all at one planet, which is silly. If you're making a massive 50-ship order there's no reason you can't distribute it all around your empire via the unified construction screen (the pick-axe looking button) and then go into your F10 Ledger and fleet those ships up while they're under construction. While they're STILL under construction you could give them a home base, and make sure the fleet is automated.. then you're massive 50-ship build order will get done fast and assemble where you want it.
Obviously for smaller orders or situations very close to the frontlines, you might want to concentrade your build orders at one space port, but other than that there is usually enough time to spread it out.
Once again, these are just my observations. There is no wrong way to play.