I hate to reply to myself for the millionth time....
I looked for the Keres attack in the Scheveningen and I did not find any problems for Black although most consider it the critical test for the Scheveningen. Here is the line:1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 e6 6. g4 h6 7. h4 Nc6 8. Rg1
d5 9. Bb5 Bd7 10. exd5 Nxd5 11. Nxd5 exd5 12. Qe2+ Be7 13. Nf5 Bxf5 14. gxf5
Kf8 15. Be3 Qa5+ I hope there are some improvements for White or I'm missing something because if not, I'm not sure why Scheveningen players would use the Najdorf move order to transpose.
I've also looked at the e6 response to Be2 and Be3 in the Najdorf, thus going to Scheveningen territory. I've gone over hundreds of variations with engines and databases and I just seem to get much worse positions than in the e5 Najdorf with what I consider best play. (which was always = eventually in the normal Najdorf) Even less aggressive moves seem difficult compared to the normal Najdorf: See 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 e6 6. Be3 a6 7. g4 h6 8. Bg2 Nc6 9. h3 Ne5 10. Qe2 g5 11. f4 gxf4 12. Bxf4 b5 13. a3 ? (I tried many variations here but it was usually slightly better for White.) Thus, I think many of those using the Najdorf move order do so because they enjoy the queenside counterplay a6 might provide and not necessarily because they think it is objectively better than the proper Scheveningen. I definitely do not think, now that e6 is better than e5 (best imo) in the Najdorf or that using the Najdorf move order gives an objectively better Scheveningen. But, my mind may change as I gather more evidence. PLEASE ENLIGHTEN ME HERE!
Now I'm starting to wonder what would be best between the Scheveningen (proper) and Najdorf (with e5). Of course, it's possible that they are equally good and a matter of preference. For example, I tend to like the Najdorf more because it seems to offer even more counterplay on the queenside. But the Scheveningen also gives a lot of counterplay.
BTW: If you're wondering why e5 is not played more often in the Scheveningen, see this amazing series of moves:
1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 e6 6. Be3 a6 7. g4 e5 8. Nf5
g6 9. g5 gxf5 10. exf5 d5 11. gxf6 d4 12. Bc4 Qc7 13. Qd3 dxe3 14. O-O-O exf2
15. Bxf7+ Kxf7 16. Qd5+ Kxf6 17. Ne4+ Ke7 18. f6+ Ke8 19. f7+ Ke7 20. Qd2 Qb6
21. Qg5+ Kxf7 22. Rhf1 Bh6 23. Rxf2+ Ke8 24. Rd8+ Qxd8 25. Qxh6 Qe7 26. Nf6+
Kd8 27. Nd5 Qe6 28. Qg5+ Kd7 29. Qg7+ Kc6 30. Rf6 Kxd5 31. Rxe6 Kxe6 32. Qxh8
Nc6 probably draw but Black could have gone wrong and gotten mated many many times.