EDIT: Didn't click that D&D has different backgrounds and this book probably doesn't so in reality the number of different options for any trait that has 6 options in D&D you could have would be the No of backgrounds multiplied by 6 which is a lot more than just 6.

I think a decent chunk of the D&D options for your characters are 6 options (so if you want to randomise a D6) as well. It's not all of them but generally there's a few D6 / 6 option tables for the D&D characters. Like the entertainer, which uses 10 for routines (but you can choose 1 - 3 routines), 8 different personality traits but 6 options each for flaws, ideal and bonds. More is obviously better to avoid repetition but that combines to quite a few different combinations. I guess maybe it also depends how many tables are used to form the background of a character.
Again more is still nicer, but quite a few combinations can come out of enough tables even if more than half of them are 6 option / D6 tables.