Two personal anecdotes to go with this.
1) I used to get excited when I'd see the phrase "Willing to train the right candidate" for a job I'd genuinely want to do. I'd bust out my A Game for the cover letter, telling them I'm the right candidate because I'm actually interested in the field, would find the work rewarding, have background knowledge or interests that would help me learn more quickly, whatever. Very rarely would I get calls from those listings to set up an interview, which means even though in my mind I'm the right candidate, in their mind, they're looking for something else.
2) A few times, I've been offered supervisor/management positions for insultingly low amounts. As in, they'd be pay cuts to what I'm currently earning but I'd be expected to take on 4x the responsibility and the stress and worry that comes with it. I think for larger companies, there's a disconnect between what HR is willing to pay compared to what hiring managers seem to think is good pay, because in almost all of those instances, when it finally came down to pay, hiring managers would talk wages almost apologetically.