You’re correct that training for mixed climbing will have great cross over to training for straight rock climbing. Both these activities involve full body strength with the focus on core and upper body. Developing a high level in either one will allow you to make minor adjustments in the routines to hone the skills in the other. For instance: While grip strength is a key ingredient of both of these the grip technique differs so you’ll need to develop those specific strengths to maximize the performance in each. That being said, if your limitation is more in core and shoulder/arm strength then there will be nearly 100% transfer from one type of training to the other.
The statement you refer to in TftNA about not being able to train skills and aerobic capacity largely holds true with some minor exceptions. If one’s base level of aerobic fitness is really low then even doing longer approaches to alpine routes will improve that and if one is climbing at more modest grades then it is possible to make gains in both aerobic fitness and skills/strength at the same time. The fitter you become and/or the higher your climbing level the more difficult it becomes to improve either one and since there is almost no transfer of training effect from long runs or hikes to climbing strength/skill (they are almost diametrically opposed from a physiological perspective), training one will take away time from training the other. So when one begins to reach their own personal limits in either of these two areas adjustments to training and sacrifices will need to be made. As you approach your limits you’ll need to adopt a periodized approach where for a time you focus on one or the other quality and reduce the training for the other to a maintenance level.
This is why we will probably never see someone climb 5.14 at 8000 meters. The demands for these “events” are just too divergent.
I hope this makes sense.