Oh the pool is also limited. You can't give it to certain players parents (such as the weakest players or you'll get blow back on the playtime, if there's more than 1 keeper either of them, if there are 2 equivalent strikers battling it out for the starter either of them, if the roster is over 18 any of the nondressers), you don't want a difficult parent that's going to challenge you, you don't want a knowledgeable parent that's going to raise questions how you do things, and you can't use the absent parents or the disorganized parent or the loud parent. Given the shortage as a result, the incentive structure is to bribe the TM (because as you point out no one else wants to do it).You guys have run into some bad apples. I've only had one out of the 17 TMs bt my children act this way and the coach and team hated the particular TM because of that. Coach couldn't get rid of him because no one else wanted to be TM and no one wanted the "benefits" enough or disliked him enough to take on the responsibilities and work. While I agree there are definitely some benefits to TMs because they are the ones communicating with the coach a lot, they generally do not have more sway about play time than your average complaining parent.
There's a reason we don't have a line of people waiting to be TMs. Have you ever heard of parents fighting to be TMs or asking to co TM? No...bc all these "benefits" aren't worth the effort required to be TMs.
It's also not true they don't have more sway about play time. I once knew a manager that made it her mission and succeeded to use her position to make her kid the sole No. 1 for the team. Nothing but a mama bear looking out for her kid, but that's the inherent conflict of interest. The position carries enormous potential power for a machiavellian with a weak coach or a coach uninterested in dealing with management....thankfully most people are not like that.