If you are going to attack a Yonko, and if also you need to make an alliance for it (which means you are not going to play fair and square), then you need to choose the weakest Yonko as you are willing to work with other pirate groups to accomplish your goal, that would be the safest bet.
So the question is, why Kid-Killer-Hawkins alliance wanted to attack Saint Shanks (4 billion bounty), instead of BB, who at the time only had 2.2 billion bounty.
Perhaps right now its a toss-up between Saint Shanks and BB, as BB got 3.99 billion bounty now, so choosing Saint Shanks or BB wouldn't make any difference
right now.
But this was before BB got his second Yonko bounty, so BB had only 2.2 billion yet, that alliance wanted to go after 4 billion bounty Yonko, instead of going after 2.2 billion Yonko.
What could be the reason?
Killer knew who was the strongest pirate is,
So perhaps Killer also knew BB > Saint Shanks? Even though BB had lower bounty.
Option A: They thought Kaido > BB / Big Mom > Saint Shanks.
Option B: Kid's magnetism ability is a good counter vs. Saint Shanks's sword, they probably didn't think BB > Saint Shanks, but they relied on that.
Option C: Kid wanted revenge for his arm so bad that they wanted to go after Saint Shanks instead of BB.