This list excludes cable show wins, since some shows do not award #1s to those who do not show up, like BTS or IU who are beyond that stage.
It also excludes those who have had no wins since the KPop era began in earnest on Sep 2007 with Big Bang's Lies.
JYP qualifies because his The House you Live one in Dec 2007, after the KPop era began.
Turbo qualifies because its Live, for the 20th year anniversary, won in 2016.
Cho Yongpil qualifies because his Bounce won in 2013.
1. BTS 121 wins. Most wins at Music Bank and Music Core.
2. IU 91 wins. Most wins at Inkigayo, because of its system of exiting a song after 3 wins.
3. Cho Yongpil, 78
4. Twice, 77. Nayeon has 4 wins.
5. SNSD, 74 Taetiseo has 4 wins.
5. Exo
7. Big Bang, 70
8. Kim Jongkook/Turbo, 69
9. Im Changjung, 52. He qualifies since he has had hits in 2010s
10. Red Velvet, 46
10. Shihhwa
12. Psy, 42
13. Super Junior, 40. I don't know whether it includes all of its many iterations.
13. Shinee
13. Beast/Highlight
16. BlackPink, 38
17, Ive, 36
18, Gidle, 34
19, TVXQ/DBSK, 33 . JYJ members are not allowed to show up in official broadcasts so no wins for them.
21. DJ Doc, 30. It won with I'm Like That in 2010.
22, GFriend, 29
22. Wonder Girls
24, Sistar, 28
24. 2NE1
24. Taeyeon. With her 74 wins as SNSD and 4 wins as Taetiseo, that puts her at 106, next to BTS and over someone who contributed nothing to KPop.
27. Itzy, 27
27. APink . Jung Eunji has 1 Inkigayo win, which makes her wins 28
30. Wanna One, 24. Kang Daniel has 10 wins, making his wins 34Wo
31. NewJeans, 23
32. Lee Hyori, 21. As Finkl she has 30 more wins, making it 51.
33. NCT Dream, 20
34. NCT 127, 19
35. GDragon, 18. With 70 Big Bang wins that makes his total wins 88.
36. CNBlue, f(X), LeSserafim, Mamamoo. 17. Hwasa has 7 wins, making her wins 24. Jung Yonghwa has 3 wins, making his wins 20.
40. The Boyz, 16.
41, Got7, T-Ara, Davichi, Zico, aespa. 15.
I stop here.
Honorable mention -
Taeyang - 12 wins, but with Big Bang wins, 82
Sunmi - 10 wins, but with Wonder girls wins, 39
Jungkook - 8 wins
Jimin and Taehyung - 2 wins each.
There would be wins from individual members of acts named above, but I cannot count them all.
Revised top 10 win count
1. Jungkook, 129
2. Jimin and Taehyung, 123
4. BTS, 121
5. Taeyeon, 102
6. IU, 91
7. GDragon, 88
8. Taeyang, 82
8. Nayeon, 82
10. Cho Yongpil, and Tiffany and Seohyun of TTS - 78
Fin.