Domdaniel: <Ulhumbrus> The mating line after 30.Rf1 Qd6 31.Nxf5 is a real beauty. These days, anyone can get an engine to churn out a forced mate - it's precisely what the machines do best - and some people might even persuade themselves that the position is an 'easy' win for Black as a result. But it was an astonishing piece of brainpower by Bronstein, Keres, or both.
I'd already thought that 30.Rf1 was relatively best for White, and certainly better than the move played. The reasoning is simple: to bolster the f3 Bishop. After 30.Re1 in the game, only the Nd4 supports it, and a Knight move allows mate in one. But perhaps after 30.Rf1 White can do something useful with the Knight?
It seems not. Your Keres line convincingly refutes 31.Nxf5. And 31.Nb5 is even worse - the Black f5 pawn contributes to a quick mate after 31.Nb5 Bxf3+ 32.Rxf3 Qd1+ 33.Kg2 Rd2+ 34.Kh3 Rxh2+ 35.Kxh2 Qg1+ 36.Kh3 Qh1#.
It's essentially the same idea, without the final flourishes needed after Nxf5. I suspect this is how the Nxf5 line was found in the first place -- solve the more straightforward mating problem (with f-pawn) first, then dig deeper to see if the same method leads to a win without the pawn. Engines have killed the artistry of such processes.
Does White have any other tries after 30.Rf1 Qd6 ...? Not much. Perhaps exchanging Bishops with 31.Bxd5 Qxd5+ 32.Nf3 staves off immediate disaster, and is almost the only way to save the Knight. But White just loses mundanely after 32...Rc8 -- he never gets time to launch a counterattack on f7 or h7, and the pawn deficit makes the ending hopeless.
You mentioned centralization as a key component of Bronstein's win, which is true. But tempo and initiative were also crucial. Moves such as 30...Qd6 -- centralizing the Queen *and* gaining tempo by attacking the Rook -- prevented White from conjuring up the sort of attack he must have envisaged when playing 16.e4. Botvinnik was simply never given time to settle.
This is apparent right to the end. A 'normal' Queen-vs-Rook+Knight ending could have taken a long time to win, but Bronstein made it look easy with ultra-precise tempo-gaining moves such as 34...Qb4!, 38...Qf2! and the beautiful 39...f6. White never gets time to play Rxe4 -- at the end, if he tries, he either gets mated (40.Rxe4 h5+ 41.Kh4 Qxh2#) or loses both pieces.
Botvinnik got positional compensation for his pawn sacs, particularly the first. But he never quite got enough initiative to compensate, and Bronstein made the most of his chances. Great struggle, beautiful game - and invisible symphonies behind the scenes, in the notes. What more can we ask for?