If you can't hear in tune you can't play in tune period. It is the same thing. Learning to hear where the note is and where its going is exactly the same as putting your hand in the right spot. The bass' positions move all the time. Your ear needs to be able to compensate for it. There are more players with "poor" left hand technique and a good ear that play with good musicianship than the other way around. If you don't teach aural skills the left hand will never develop.
Besides notes don't exist on their own they exist in relationship to others. I've said it before. A B in G chord is not the same as a B going up to a C or down to an A. This is true no matter how atonal you get. Your ear needs to know that and adjust. Intonation is both components the hand and the ear and nothing less. To take one from the other is just not sensible.
I do hear where you're coming from in regard to the other instrument thing. But bass guitar is fixed in equal temperament though where as double bass is capable of so many different tuning systems. As such in most jazz contexts equal temperament will suffice, but in new music, classical music and other forms of music systems such as just intonation, Pythagorean mean temperament and microtonalism just to name a few are used. If you are teaching exclusively jazz than equal temp is fine. But what do you do about the rest? That is why, like you said a wholistic approach is necessary. In a lot of ways my college musicianship classes were nearly as important to my development as bass lessons. Scratch that, equally as important. My teacher makes me sing everything I don't play in tune. Everytime, the passage I play out of tune, is being sung out of tune. Once I tune it up singing, I play in tune.
Playing bass is just playing bass. Playing music is the whole enchilada. In the end that's what its all about right? YMMV.