Not fully thought through, but it's so simple that maybe it doesn't need to be thought through too much.

Get rig of individual coaches altogether.  Replace it with a coaching budget that can range from $0 to $20m.  Actually, it would be replaced by four separate coaching budgets, each of which covers your players at all levels (ML through RL):

Hitting (ranges from $0 to $5m)
Pitching (ranges from $0 to $5m)
Fielding (ranges from $0 to $5m)
Base Running (ranges from $0 to $5m)

For each category, a $2m budget gives you average development (of younger players) or average regression (of older players).  Go below $2m, and you risk slight regression of ratings in that category (or accelerated regression for older players).  $0 gives you a lot of regression.  Go above $2m, and you get above average development for younger players (slower regression for older players), with $5m being maximum improvement / minimal regression.

Why do this?

1)  Nobody likes coach hiring.  Many people hate it.

2)  The current system is built on smoke and mirrors: there is no objective way to quantify how good "good" coaches are, or how bad "bad" coaches are, other than anecdotal observations.  This gives you more of a "hands on" approach to knowing what your budget is buying you.

3)  You can tailor your budget to your specific needs.  If you have a fully developed veteran pitching staff and weak pitching prospects in your system, and a solid crop of young hitting prospects, you can go $3m on pitching and $4m or $5m on hitting.

Looking at my three worlds, a typical coaching budget is $10 or $11m.  Going "average" in the four coaching buckets would cost $12m, so that's low impact (on average) for most people.  But seeing that you have more control over the impact of coaching, owners now might choose to invest more in coaches than they did previously, which takes away budget from some other category.  More decisions means a little more strategy.

Another possibility: similar to the +/- $4m maximum change in other budgets per season (the 4 scouting budgets, medical and training), you can limit the amount of change in the coaching budgets from season to season to $1m per season, thus preventing huge swings from season to season.  This conforms to the "planning for future seasons" aspect of the game (actually, it introduces it to the coaching budget).

Is this realistic?  Not at all.  It's a deviation from "real life".  But it might be an improvement to the game.

Thoughts and feedback welcome.

Does it really "dumb down" the game?  It pretty much brings coaching to the same level of scouting, medical and training, where you know that the more you budget, the better service you get.  And vice versa.

To turn your comments around, changing scouting to hiring individual scouts with various ratings (ability to project hitting, ability to project pitching, etc), or changing training to hiring individual trainers with various ratings (strength conditioning, injury prevention, etc.) would be an improvement to the game.

Removes "bargain" shopping.    I never go over 9m and feel just fine with my development.    I won't get that under your system.

I used to grind coach hiring out. When you start playing this game you think sure it's logical, you want the best coaches you can get, you must compete with other owners for them.
After you play and learn a bit you start to realize the disconnect between ratings and money, the inconsistencies in logic, the nagging feeling that maybe it's all just a red herring by the developers. To be frank, it feels like a make work project to me. Eventually I decided that the only "must" in coach hiring is to avoid your coaches being total crap. So you learn where and when to go cheap.
So to paraphrase Mike yeah, at this point I DON'T want coach hiring to be more meaningful or effective.

Thinking about this further, no.     You're essentially turning it into training.     Maybe you skimp on BR, if you're punting SB, at 2m but the others just about have to be 4-5m.   So, IMO, you're making coach hiring a 14m minimum category.    No thanks.