If everything is CNC today, how do end up being that far off?
Simple answer is tolerance stacking.
Longer answer is still tolerance stacking, but with more words. Every single screw hole has a dimension from one or more surfaces on the body of the bass. So does the neck pocket, and the routing for the pickups, control cavity, etc.
All of these have an amount +/- they can deviate from that dimension. The tighter that tolerance, the more time and cost you incur holding that tolerance. A CNC machine is very good at holding tolerances, but it is not, nor can it ever be, perfect.
So as a designer* we have to decide what areas need to be held closest, and which ones can vary. In the case of a Jazz bass, I'd try to nail the neck pocket, and the pickups and bridge will all be based on that pocket, because those are more location critical based on distance from the frets, alignment with the neck, and so on. The control cavity can more or less be wherever, so who cares.
The pickguard is kind of the same. By itself it's really of no importance, except that here, you have a choice to make. It's relieved to go around the pickup, and to fit around the control plate. So which do you favor? Well, since the pickup is an important piece, you probably want the pickup opening to be favored, which means that the control plate isn't.
So, you have a tolerance for the neck pocket, which impacts the pickup position which itself has a tolerance, which impacts both location and angle of the pickguard, and it's interface with the control plate, which of course has it's own location tolerance.
And this doesn't even get into the fact that both pickguard and control plate have their own overall dimensional tolerances from their separate manufacturing processes that will impact all of the above. For example, even if all the above mentioned holes and routings in the bass body are 100% accurate with no deviation, if the opening in the pickguard is off and at a slight angle, then it's interface with the control plate will be off.
Some of this can be helped with order of operations, like maybe not drill the screw holes for the pickguard until the pickup placement is set (using a template over the pickup, perhaps) or by doing some final fit/finish work by hand, like trimming a bit off the pickguard so it doesn't look out of place, or reshaping the end of the control plate, etc. But that takes a lot of extra time and ends up with bespoke parts that can't always be easily replaced later, as any replacement would need to be fitted as well.
TL : DR- Tolerances impact tolerances, machines aren't perfect, and getting as close as one can will cost more in time, money, or both.
*- I'm a mechanical designer who has done work with stamped, bent, machined, etc bits of metal and plastic. There is almost always an option to hold tighter tolerances, but cost is a big factor. If nothing else, the machine runs slower to keep those tolerances. Some machines are better than others of course, but those usually also cost more. Always about the $$.