I have to respectfully disagree about a couple of your concerns.
First, about strategy, you could still contact another team and, instead of discussing a mutual TIE, you could agree to play your secondary players. (In fact, if you did that, it would be much harder for other teams to figure out that you had such an agreement than it is now, since your box score and roster would have to be studied to figure out if the reserves were starting. At present, other teams can easily see if you TIE.) Agreeing to play your reserves doesn’t have an affect on enthusiasm, but it does keep your starters from getting too tired, which is also an important factor for you as a manager.
Second, the only “automatic decision” that having a coach would necessarily take away (other than the impact of the current enthusiasm system) is Enthusiasm. Without getting back into the realism of Enthusiasm (there seem to be plenty of other treads on this, on which I already acknowledge my opinion is decidedly against Enthusiasm as a realistic or desirable part of this game), I think adding a Coach would actually increase strategic potential, since the ability of your coach would now involve a financial aspect, as well as your preferences in your coach’s attributes and abilities. (The details of what attributes a coach would have would obviously be the prerogative of the very capable game developers, who have obviously done great work in getting this game to where it is now. If it wasn’t such a great game, I wouldn’t even care to share my thoughts on what I think would make it better, and there weren’t be constructive responses on the suggestions from other caring participants. But I digress…) As things stand, there are already automatics in how your team is coached. Your ability to select an offense and defense for a game probably won’t go away with the addition of a coach. You can still give your coach that direction. But it will now be your coach that will inspire your team to play hard (or not). If your team has been winning, any coach can inspire such a team to keep winning, but not every coach can keep them sharp. If your team has been losing a bunch a games, it takes a good coach to get their confidence back, or maybe you’d need a new coach if your team loses respect for your coach. There are lots of angles the game developers could take with a coach, but I think creating such an element in the game, with one bold move, could simultaneously remove one of the very few questionable aspects of the game and add another integral strategic element that would make the game that much more interesting.
Don't ask what sort of Chunks they are, you probably don't want to know. Blowing Chunks since Season 4!