Hattrick is the granddaddy of this genre of web-based sport sim games. BB-Charles spent a lot of time there, and a lot of the people recruited to help create this game also came from there. A lot of the things I enjoy most about this game are in large part because it's an improvement over how the same things were handled on HT. Some of the changes ended up not working out, of course.
I tend to agree that the auction system for staff isn't optimal, because an auction implies that the asset being purchased has some value but there's no way to recover some of that value by selling the asset later.
As far as how much some people pay for a trainer, it's the same as some people paying millions for the absolute elite trainees - it's a premium because of the scarcity of the specific thing desired. Thankfully, most of the people paying that amount of money are doing so because they are aware of the costs and believe that it's worth it, to them, to spend that amount of money for the relatively small boost it gives them compared to the alternative.
I don't think generally teams go through 2-4 trainers a season. I've had seasons where I'd go through double digits in PR managers to get the home court or road advantage, but I wouldn't spend more than a thousand or two, plus the five to seven thousand severance, and I felt like the slightly improved chance of winning was worth that. I think most trainers are probably replaced every season and a half or longer.