Do you need to buy some sort of cargo bay for your ship to be able to carry cargo at all, or do the supplemental cargo bays only cost points because they give you some sort of advantage?

I find it hard to believe that in a ship capable of housing 10,000 people, the designers wouldn't include space to put some crates unless the customer was willing to pay extra, yet I find no rules on the cargo capacity of various ship designs.

Can anyone shed some light on this?

Most ships have a decent number of small cargo holds throughout the vessel, but these are a matter of necessity. The Components available are representative of large scale cargo holds, designed for the transport of very large quantities of goods.

So, if you don't buy a cargo hold of some type, you would generally be unable to haul substantial amounts of cargo. But you would still be able to carry small, high value cargo, and almost all personal equipment.

It's the difference between having storage rooms and closets scattered around the ship for storing goods close to where they are needed and having a few bays that are several hundred thousand square feet each.

You can move cargo in the storage rooms but the cargo bays are much more efficient.