Why not 4.e3 Bxc3+ in the Nimzo-Indian? Why is 4.e3 Bxc3+ almost never played in the Nimzo-Indian, with idea of 5.bxc3 c5, considering that this is a relatively feared move after 4.e3 c5 5.Nf3 Bxc3, et cetera (Huebner Variation), so that a lot of White players switched to 5.Ne2 to avoid this system in recent times? 

[fen ""]
[title "Nimzo-Indian Defense with 4. e3 Bxc3+"]
[startply "7"]
[startflipped "1"]

1. d4 Nf6
2. c4 e6
3. Nc3 Bb4
4. e3 Bxc3+
5. bxc3 c5


Same question from a different perspective: is one tempo that important in a relatively closed position? (e.g. 4.a3 Bxc3+ is generally considered a good game for Black). Then why shouldn't it be after 4.e3 Bxc3?
In this case, one tempo is important due to the concrete nature of the current position. White doesn't have to use it to play Nf3:

4.e3 Bxc3 5.bxc3 c5 6.Bd3, and if Black plays in the style of the Huebner with 6...Nc6 then White has 7.Ne2! and now 7...d6 8.0-0 e5 9.Ng3! gives White an edge (Stockfish says around +0.60). His knight controls the key e4- and f5- squares, and an f4 push is coming soon. This position is a major improvement for White over the normal Huebner system, where instead of playing Ne2-Ng3, White plays Nf3-Nd2 (to avoid Black's threat of playing the ...e4 fork). A knight on g3 can become an active attacker on the kingside, while a knight on d2 just blocks in the c1-bishop.

Note that if Black refuses to play in the style of the Huebner (6...Nc6, 7...d6, 8...e5) then White plays an early e4 push and gets a crushing position in the centre.