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I didn't expect a level 7 doctor to perform a miracle, but I expected a player who at that moment had 6-11 days of injury to recover in 6 days. It shouldn't be a miracle if you buy THE HIGHEST LEVEL OF DOCTOR. I didn't ask to recover in 4 days

Doctors are mostly useless, dude. You pay them a fortune and they give you almost nothing in return. Your reasoning makes total sense, but it's not how things work here. The higher the level of staff, the more exponentially expensive they are and the less exponentially they give you back. I don't think this is a huge problem in general, like in training, but in the specific case of injuries this just adds exponentially more outrage to what is already outrageous.

His game shape likely has deteriorated and will need a week+ of minutes to get back to just where he was. The game assumes no practice or training while injured. What's even more strange is a player's game shape drops after you purchase him from the market.

Game shape drops after a sell/purchase is alright, it's a proper way of dealing with daytrading and other suspicious market practices.
But... if there was a way of making injuries fair and realistic, they should be definitely linked to game shape... higher levels of game shape should prevent or stop injuries (level 9 should never lead to injury, level 8 extremely rarely, level 7 less rarely and below 6 injuries should happen often)... mastering game shape is hard and should be rewarded, this would be fair and realistic, way more than the random crap which has always been injuries in BB, probably the worst (of the very few bad features) feature of the game.

But... if there was a way of making injuries fair and realistic, they should be definitely linked to game shape... higher levels of game shape should prevent or stop injuries (level 9 should never lead to injury, level 8 extremely rarely, level 7 less rarely and below 6 injuries should happen often)... mastering game shape is hard and should be rewarded

Unless you have just bought a player it's near impossible to have someone in less than 7 GS, and most players are in 8-9 GS all season (after the first couple of weeks). GS is very easy to manage for two games/week, it only seems like a challenge for elite teams trying to win three games every week. But even then I rarely see their players in low GS. The above is basically just turning off injuries.
I would like to see a little more variance in GS updates, but I suspect that would be a minority opinion

The higher the level of staff, the more exponentially expensive they are and the less exponentially they give you back.

My understanding was the difference in skill between a level of staff is a roughly linear improvement, although I'd have to double check that.

Salaries seem to also be linear, roughly you might pay $5k for a level 2, $12k for a level 4, $20k for a level 6 doctor. Higher level salaries do increase at a slightly higher rate, but the initial fee for non-coach staff is very small so you can just replace them more often.