The variation beginning 4.e3 Bxc3+ is not popular, but it is better than its reputation, and it's a very efficient way of cutting out a lot of theory if you're just taking up the Nimzo-Indian as Black. It hasn't been tried and found wanting; it just hasn't been tried (very much).
Essentially, Black would like to set up a darksquare pawn structure and would be happy to transpose into the Huebner Variation should White be so inclined. As II has pointed out, White's main way of avoiding the Huebner Variation is to choose Ne2-g3 instead of the more direct Nf3. But Black can generate pressure against White's center with or without ...e5, and in the Ne2-g3 lines he may well adopt the setup 5.bxc3 d6 6.Bd3 c5 7.Ne2 Nc6 (or even ...b6) 8.e4 0-0 9.0-0 b6 when he has ideas like ...Ba6 and ...Na5 or even ...Nh5 and ...Qh4. Stockfish 10 chews on the position for a while and coughs up an evaluation of 0.00. That doesn't mean the position is actually equal (see the discussion in Sadler and Regan, Game Changer, for some insight on what that 0.00 actually tells us), but it does mean that if you're a human being and you like Black's position and think you understand it, you should feel free to try it out.
At GM level, the Armenian GM Ashot Anastasian (d. 2016) frequently employed 4...Bxc3+, and it shows up occasionally in the practice of GM Paweł Jaracz, GM Leonid Yudasin, GM Dmitry Andreikin, GM Chanda Sandipan, and GM Roman Ovetchkin. In the Mega 2013 database Black scores a respectable 44% with it out of 166 games at master level (2200+ for both players).