Because John and Timothy are more important characters than the mayor. I never said that about Jeremy anyway, I only said the Taxman and the mayor were occasional characters. How does that equate to Jeremy being one as well? John lives with Anna, so the chances of him bumping into her normally, are far greater than Jeremy, who relies on Anna being able to do most of her job, without any input from him. I don't know about you, but I had a managerial position in a company office, and on average I saw my boss about once or twice a week, so why should Anna be any different with Jeremy? Timothy works under Anna, in the same part of the office, so she sees him every working day, whilst Jeremy is either busy in his own private office, or in a meeting in another part of the city. You're always going on about the game being more rational, but that appears to go out of the window, whenever the characters you like, don't monopolise the gameplay.
In Chapter 1, it was different, because Anna was Jeremy's PA, so you would expect her to see him far more. He made her a manager, so she could go off and do her own thing, without him having to get involved all the time. That's what the bosses of companies do, they delegate, so they can concentrate on all the most important stuff. If Anna was spending time with Jeremy every working day, whilst she was supposedly the manager of a separate department. That would be irrational and unrealistic, because in the real world, it rarely happens that way.
This is all incredibly obvious, to anybody who doesn't play this game with blinkers on. So I'm not going to repeat this ad infinitum. As I said above, you're welcome to believe what you want to believe.