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Duets wise, Abby hasn't given out duets like Brooke and Kenzie and Paige and Kendall is because it's expensive to enter numbers like duets and trios and Abby probably wants duets which are more likely to win first place like a Maddie and Chloe duet or a Chloe and Paige duet. Also another reason might be age difference. Brooke is 15 and Kenzie is 9. Paige is almost 13 and Kendall is 10. 

Solos wise, it's probably the same reason.Solos are like $85 dollars each and costumes are also pricy, like Chloe's costume for " My Obesession " was around $600. So yet again, Abby wants her best shot at first place so that's why Maddie, Chloe and Kendall get more solos than Nia, Paige and Brooke.

Group numbers wise, the reason Brooke and Kenzie are often disincluded is because with younger dancers like Kenzie, her technique isn't up to base with the others and sometimes the number might be about something more mature so the judges might think it's not right to have her in the number. And with older dancers like Brooke, She may look quite out of place even though she not tall, she does look older. And at some competitions she would be to old to compete in the Juinor category and the group could be disqualified.

On my behalf I don't really agree on it, but that's pretty much how it works.