For my methodology, I loaded up EDHRec, went to the 2-year data as a table, expanded it down to the top 300 entries, copied that over to a google sheet, manually re-populated the color IDs that didn't transfer as part of that, and the summed by color ID and ranked them.
The results were as follows:
1 WUBRG 61361
2 BG 37558
3 BGU 34726
4 RWB 33131
5 GU 32893
6 UB 31760
7 UR 29823
8 WUB 26950
9 UBR 26610
10 RGW 24321
11 BR 22600
12 GWU 21524
13 WB 21192
14 R 19858
15 B 19848
16 URW 19717
17 GUR 19019
18 GW 19012
19 RG 18717
20 BRG 17724
21 U 16300
22 G 16106
23 RW 15016
24 WU 14518
25 WBG 13742
26 GWUB 10500
27 RGWU 8137
28 W 6347
29 UBRG 4091
30 C 3812
31 BRGW 3750
32 WURB 1205
1) Five color is the most popular combination, even after the banning of Golos (who isn't included in the source data despite having been the previous most-popular commander).
2) Four color combinations are relatively unplayed, likely due to the lack of different options. Each has 1-2 non-partner commanders and then a couple of partner pairings, and they make up five of the bottom seven results along with mono-W and Colorless. This is despite Atraxa being literally the second most popular commander.
3) UW is the least popular two-color pair and in the bottom ten overall. The other three blue pairs are at #2, #3, and #4 among two-color pairs (after only BG, which has several very popular options in Lathril, Blade of the Elves and Meren of Clan Nel Toth).
4) WBG is the least popular trio, only beating out the 4-color combos, W, and C. This somewhat surprised me, because I thought options like Nethroi, Ghave, and Karador were perennially popular. I suppose though, that most of the other shards and wedges got additional commanders in various sets in the past few years beyond just Ikoria, while WBG's only recent options have been Ikoria + Kethis.
Overall, it seems like the two biggest factors for a color pair's popularity are the popularity of the component colors (stuff with at least two of U, B, and G generally do better than those without that) or specific very popular commanders (like Kaalia/Edgar/Marchesa for WBR).
So UW suffers in both of these accounts. It's got blue, but lacks green or black. And unlike UR, it doesn't have a top 20 commander like Niv-Mizzet, Parun, with Brago barely scraping into the top 50. after UR's second most popular commander.