Understanding Carlsen's resignation in the rook and pawn endgame vs MVL Why did Carlsen resign in the position shown below? (blitz game played in the London Chess Classic GCT Finals)

Can't white help the pawn queen after Ke3 and Kd3 then Kd4? I must be missing something.

[Title "Magnus Carlsen-Maxime Vachier-Lagrave, London Chess Classic GCT Finals, London England 12/02/2019"]
[FEN ""]
[startply "108"]

1. d4 Nf6 2. Nf3 g6 3. Nbd2 d5 4. b3 Bg7 5. Bb2 a5 6. a4 O-O 7. e3 Bf5 8. Be2 Nc6 9. O-O Nb4 10. Ne1 Ne4 11. c3 Nxd2 12. Qxd2 Nc6 13. Nd3 e5 14. Nxe5 Nxe5 15. dxe5 Bxe5 16. Rfd1 Qd6 17. Ba3 c5 18. Qxd5 Qxd5 19. Rxd5 Bxc3 20. Rad1 Bb4 21. Bxb4 cxb4 22. Bc4 Be6 23. Rb5 Rfd8 24. Rd4 Rac8 25. Rxd8+ Rxd8 26. Kf1 Bxc4+ 27. bxc4 Rd2 28. Rxb7 Ra2 29. c5 Rxa4 30. Ke2 Ra3 31. c6 Rc3 32. c7 Kg7 33. Ra7 b3 34. Rxa5 Rxc7 35. Rb5 Rc2+ 36. Kf3 b2 37. Rb6 h5 38. h3 Kf8 39. g4 h4 40. g5 Ke7 41. e4 Kd7 42. Ke3 Kc7 43. Rb5 Kc6 44. Rb8 Kc5 45. f4 Kc4 46. f5 Kc3 47. Kf4 Rg2 48. fxg6 fxg6 49. e5 Re2 50. Rb6 Kc2 51. Rc6+ Kd1 52. Rd6+ Kc1 53. Rc6+ Rc2 54. Rb6 Rc4+
Intuitive plan

Notice that black's last check is pushing the white king one row away from their passed e-pawn. Once black promotes the b-pawn, white will have to give up the rook for it. After which white's king is simply not in position to cover the advance of the e-pawn and therefore additional tempi will have to be spent with king moves to try and reach the pawn, during which the rook can first simply capture white's h-pawn and only then sacrifice itself for the e-pawn. Then black's h-pawn promotes and wins trivially. Now let's see how all this pans out concretely (no matter how strong the intuition might be, in endgames one must always primarily rely on concrete calculations in order to realise whether our ideas or plans can actually be optimally implemented).

Annotated diagram

 [title "A simple continuation showcasing why white is lost here"]
 [fen "8/8/1R4p1/4P1P1/2r2K1p/7P/1p6/2k5 w - - 0 1"]

 1. Ke3 b1=Q 2. Rxb1+ Kxb1 3. Kd3 (3. e6 {blunders the e pawn away} Rc6 4. e7 Re6+) Ra4 4. Ke3 {again, the pawn advance would simply leave it hanging, so white has to make king moves while not allowing black to get behind the pawn} Ra3+ 5. Kd4 Rxh3 6. e6 Rh1 7. Kd5 h3 8. e7 Re1 9. Kd6 Rxe7 {though black doesn't even have to sacrifice the rook here, but it's simply a practical way of going about it, and in-line with our original plan} (9...h2 {much more accurate continuation as we can in fact keep our rook since white's tactically losing their queen immediately upon promotion, in fact you might find this line easier to calculate} 10. Kd7 h1=Q 11. e8=Q Qd5+ 12. Kc8 Rxe8+) 10. Kxe7 h2 {and it's easy to judge that black's winning here since the promoted queen is well in time to get to white's promotion square g8 and then simply bring the king over. I'll include this sequence} 11. Kf6 h1=Q 12. Kxg6 Qb7 {cutting off the king from accessing the 7th row} 13. Kf6 (13. Kh6 Qf7 14. g6 Qg8) Qh7 14. g6 Qg8 {and now black simply brings the king and wins the pawn}