The greatest player to NOT win WCh: Rudolf Spielmann obviously.
2nd: Jan Hein Donner.
The best (imo something quite different) to NOT win WCh:
Reuben Fine. He was still improving since 1937. If it had not been for WW-II I am convinced, that he would have won the title in 1940 or 1941.
Once could say the same about Pillsbury and I think it a shame, that Lasker did not give him a match around 1900, but I also note, that Pillsbury in tournament games lost from Lasker in London 1899 and Paris 1900.
There are strong arguments for both Schlechter and Bronstein of course, but fact is that they failed on the decisive moment. Same even more for Kortsjnoj, Tsjigorin, Tarrasch, Keres and Ivantsjuk.
In fact nominating Tarrasch is a bad joke. Willempie gives a game? So can I and there are many other similar examples.
Tarrasch,S - Spielmann,R [C11]
DSB–15.Kongress Nürnberg (10), 1906
1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.e5 Nfd7 5.f4 c5 6.dxc5 Nc6 7.a3 Bxc5 8.Qg4 0–0 9.Nf3 Nd4 10.Bd3 f5 11.Qh3 Nxf3+ 12.Qxf3 Bb6 13.Ne2 Nc5 14.Be3 Bd7 15.Bxc5 Bxc5 16.0–0–0 b5 17.b4 Bb6 18.Kd2 Qe7 19.Rb1 a5 20.Rb3 Rfc8 21.Nc3 Rab8 22.Rhb1 a4 23.R3b2 Bd4 24.Nxd5 Qd8 25.c3 Ba7 26.Ne3 Bc6 27.Qe2 Be4 28.Rd1 Qc7 29.c4 Bxd3 30.Kxd3 Rd8+ 31.Kc2 Bxe3 32.Rxd8+ Rxd8 33.Qxe3 Qxc4+ 34.Qc3 Qe2+ 35.Kb1 Rd1+ 36.Ka2 Qf1 37.Rc2 h6 38.g3 Kh7 39.Qb2 Qd3 40.Qc3 Qd5+ 41.Kb2 Rd3 42.Qc5 Qb3+ 43.Kc1 Qxa3+ 0–1
In 1909 or 1910 Rubinstein should have challenged Lasker, not Janowsky, because of St Petersburg 1909. But San Sebastian 1911 already showed, that Capablanca was the man. I frankly think, that Rubinstein never would have been able to beat Lasker.
Be grateful btw, that Rubinstein never played a match with Capablanca ...
That leaves Nimzovitsj. New York 1927 showed him to be the world's third player. Since then he improved, culminating in his fantastic result at Carlsbad 1927. Note that he did not really dominate the tournament though. My argument is, that in 1929 he indeed had about the same right to play against Alekhine as Bogo. But as the 1929 match and the 1930 San Remo tournament show, Alekhine had improved even more. Nimzovitsj would not have had a chance. As Nimzo himself has said: "a couple of years ago we were all about equally strong, now he treats us like children."
Note that I a base my argument on relative strength. When it is absolute strength, then Topalov

(might be the next WCh). And my hero? Neither he himself nor I nor someone else consider(ed) him ever as a candidate for the title.
PS: Sjirov defeated someone in a match, who would become WCh within 2½ years. Who else can say something like that?