I agree with your suggestions about factors that limit the attractiveness of the role, but I'm talking about training teams were the job is training full-time. Often they allow trainers to keep up their developments skills by taking mini sabbaticals, but it's full-on training. Prep time is allocated, and often when there is marking to be done, there are graders to assist. I'm pretty sure that the pay is good enough because when we find a qualified candidate it has never been a sticking point. Hence, I would guess that I'm thinking of the 'better end' of all of those factors, and yet either the pool is small or it's very hard to find. As for TAs, Associate Professors, and Professors, we've only had limited success there. Rarely are their technical skills strong enough, and teaching skills are often shockingly poor. I can think of one trainer who was a professor previously and is truly excellent in the role. The difference? They're really into tech and they're really think about training as a worthwhile skill.

It's surprisingly hard to find technical trainers. Very few candidates make it through a phone interview, let alone an example teach. Admittedly it's an unusual combination of skills. We want people that have serious development chops, know multiple languages well (although no need to be perfect), and can teach. The pay, I believe, is good (I do it professionally). It's still stressful at times, but it's a different kind of stress. Agencies have been next to useless finding candidates because they understand none of the skills or how to screen for them. Many people in the tech world don't know these roles exist, or don't know what it takes, so if you're curious here's the kind of things you would need to do/be to make it through an interview, and land the job:

Technical
* Demonstrate clear fundamentals in your 'home' language, e.g. in Java I might ask about pass by value and how that affects code, or in C++ explore where and when you use the destructor. These are not obscure corner cases, although later stages of an interview could move to that but the technical interview is mostly done by then
* Demonstrate authenticity, e.g. have you experienced the stress of dealing with a 'sev 1' and survived to tell the tale

Teaching
* Can you stand up in front of people and engage them in learning
* Can you think on your feet and derive an answer from existing knowledge
* Can you admit when you don't know something, research the answer, and come back to the group
* Can you present information clearly

Last of all, can you do all of this with enthusiasm? I genuinely don't know if it's just a rare combination of skills, or we just can't find the people.