I'll say it again: Stiffness and stability are two different things.
If you build the neck correctly, you won't have a problem with stability. It won't warp or twist over time (long term stability) and it won't move much with changes in the weather (short term stability). The neck can be built to be stiff or to be soft. If it's built carefully, it will be stable.
Reinforcing rods or bars of graphite, steel, whatever, add stiffness to the neck. That is, it will take more pounds of force to bend it the same amount. So, if you built the neck poorly and the wood tries to warp or bend with the weather, the graphite rods will resist against that bending. The rods can't completely stop the bending, but they will reduce the amount.
The truss rod is an adjustable stiffener. It can add no stiffness, if it's loose, or a lot of stiffness, if it's tight. Tightening it adds stiffness and forces the neck to bend backwards. A double-acting truss rod can force the neck to bend backwards or forwards.
The truss rod only has a limited amount of force that it can apply. The stiffer the neck is overall, the less range of movement you can get from tightening the truss rod. If the neck is really stiff, the truss rod is useless. If a really stiff neck warps, you are out of luck. The truss rod can't help it.
If the neck is built well, and doesn't have a stability problem, then the reinforcing rods aren't necessary. They are just added weight and stiffness, and they are restricting the capability of the truss rod.
How stiff or soft you decide to build the neck will have an effect on the overall sound of the bass. That's a complicated subject by itself, but in general, a stiff neck makes the bass colder, clearer, with a flatter attack curve and minimal background coloration. A softer neck makes the bass warmer sounding, more percussive, and with more background coloration. But there are many overlaps and other factors in there. So, you may want to build the neck really stiff, or not. It depends what kind of bass you are building.
Building a neck correctly, so it doesn't have stability problems, is also a big topic by itself, but it comes down to three things:
1.) Making sure that the wood is properly dried and free of internal stresses.
2.) Cutting the wood and any lamination strips to put the growth rings and grain lines in the best orientation along the neck axis.
3.) Sealing up the wood, so that moisture from the air doesn't soak in and out as the humidity changes.
I hope this answers your question? When you get into the details, building a "good" bass neck is more complicated than it appears. There isn't any single best way; there are tradeoffs and many different approaches.