If by "Holy Trinity" you mean the 3 brands I'd be content to have replace my entire bag collection, it would be Dior, Moynat, and Hermes.
If you mean the brands with the highest visibility, it'd be LV, Chanel, and Hermes.
If you mean the top three brands with the best craftmanship, you can take your pick from Hermes, Valextra, Moynat, and Delvaux. Maybe Bottega, too.