Working specifically on independence exercises IME makes some problems go away. Definitely not all but it is very efficient to use independence exercises that others have worked out in the past.
I'm going to go out on a limb and posit the human brain is only capable of constructing one rhythm at a time. That's the only independence I'll agree with. Everything after that is a construction of patterns and coordination between limbs.
For example, you learn jazz by first playing the ride pattern against a 2 and 4 on the HH foot. You then learn all the permutations against that ostinato with your left hand (LH). And then you might figure out that all the work is really between your two hands, because the HH foot isn't doing much. So you could work through a lot of independence with just your hands, if you wanted to (eg your practice time includes what you can do sitting at the bus stop, but the soles of your shoes are soft enough to not articulate sound).
But let's include the HH foot (LF) because it's easy (we're now sitting at a drum kit). You're still thinking about
one rhythmic idea (those permutations) being applied by your left hand, against the ostinato applied with your RH and LF. If you then want to add the kick (RF) to the mix, you are trying to forget about the RH/LF ostinato, and looking at
patterns between the LH and RF. The RF is now
not an independent idea. It's part of a pattern with your LH, generally speaking (an exception would be sparse kick placement in the bar such that it really isn't part of a pattern).
A lot of the work in John Riley's books is learning common LH/RF patterns against the RH/LF ostinato.