Well, since I worked with one of the co-architects for the Brazos Co Courthouse, I can probably speak to "what were the architects thinking?"
One of the constraints was that Modern (Post-Modern if we must quibble) Architecture was in vogue. Public-project budgets, never over-rich in the first place, are doubly-complicated with courthouses. This is due to certain expectations for the appearance of courtrooms.
Which brings up another issue on appearance--change in use and function. That, coupled with changes in several technologies.
In the days of the glorious county courthouse, they were day-lit, "natural" ventilation buildings whose primary purpose was to house the county Court, and the County Offices.
To accommodate daylight, and for cross-flow ventilation, you are limited to buildings (or wings of buildings) only about 25' to 30' wide. If you need more than room that wide (like if there are two County Courts, for instance) you need additional floors, or longer wings. In natural ventilation, you also need taller floors, with 18' or 20' between floors, and not 12-15' as seen today.
The need for light/air wells, and use of multiple tall floors makes for a unique appearance. One we can see in the photo album of courthouses.
But, enter in technology and societal change. Electricity gives air-conditioned floors, so more floors within a given height are possible. Electrical lighting means that courtrooms do not need windows. In fact, dark courtrooms are at an advantage for various presentations within the courtroom.
Also, Courthouse operations virtually require proximity to the County Jail. Jails tend to need to be windowless sorts of buildings.
Ok, so that was then.
We could certainly turn the inside feces of a putative Courthouse to the inside, and set the other spaces to the outside. Jury waiting areas; jury pool administration areas, and the like could all be on the outside.
But, that would require a new from the ground up building. Which would take a bucket full of dollars, and for all the visual failings of the present CH, it's cheaper than a brand-new one.
Makes it a question of hurting one's eyes or one's County Property Tax bill.