On a project as complicated and interwoven as the Apollo system, designers of individual systems were typically just given a set of targets and told to get on with it! Due to the lead times, and constraints of project management** you were given a mass/space/power envelope and a set of performance requirements and from those you designed your system. With reliability and flexibility high up the list, much higher than capability / integration.
Because of those factors, the designers of all the Apollo systems chose proven, high reliability blocks from which to construct their systems. With it's roots in the Mercury and Gemini space projects, a lot of the electronic tech was even at the start of the project nearly a decade old, but when someone says "I want man on the moon in under 10 years" you don't start re-inventing the wheel ;-)
The system of very basic ICs on cards is incredibly flexible, and because each "chunk" is relatively simple, testing and production validation during build / assembly is much easier. The requirement to provide test hardware early in the program life (a long time before anything actually flew) mean't that it was inevitable that changes to the control logic and execution paths would occur, and that a massively modular architecture enables that to occur without significant re-certification for flight (In effect, you make a few very basic components, certify the heck out of them, and then use them in their thousands, rather than using fewer but more complex and each slightly different components!)
There are a good series of videos uploaed to Youtube that cover the status of the Apollo project through the years. As someone who thought the project was about building a moon rocket, the amount of support systems and infrastructure engineering and development is simply mind blowing. Compared to some of the test systems, building the actual rocket was relatively easy:
** imagine trying to project manage a project the size of Apollo today, even with all our computerised management systems it would be a massive PITA, in the 1960's with paper and pencil, just managing the work scope/flow must have been a nightmare!)