The rappers choose the beats. I don't think Al is holding out on anyone. Someone else might have turned down something Boldy rapped over and vice versa.
I'm not trying to sound like an a$$hole, but Boldy and Al have kind of a weird relationship where a lot of times Boldy actually doesn't choose the beats. Apparently for
Price of Tea in China he had Alc choose every single beat for that album. Not only that but Boldy didn't even pick what songs went on the album. He just recorded a batch and let Al decide what stayed or left for the final product.
For
Bo Jackson they said it was a little different and Boldy chose more on that one, but he still let Al pick the lion's share. So specifically with Boldy, Alchemist sets aside a lot of beats that he thinks would sound interesting with Boldy's voice on it, or beats where Boldy might have to push his flow (like Speed Trap), etc. Also, on 300 Fences, Alchemist had that beat as the soundtrack for a car chase, and suggested Boldy use it to tell a story about running from the law. Boldy and Alc recorded like 50 songs for
Bo Jackson and
Super Tecmo and cut it down to 25.
Murs and 9th Wonder used to do this. Murs used to fly to NC and would tell 9th, "Hey man, pick the 10 beats you want me to rock over. I don't want to have any say at all."
EDIT: But I also don't think Al is holding out either. On his new Complex interview he said he's still literally making lots of beats every single day. There's a lot of fire to go around. He has an abundance mentality where it's like, if you aren't there to get the beat when it's fresh out of the oven, then there will likely be another good one for you the next time you're around.
Interview from this week:
A Conversation With The Alchemist, 2021’s Best Hip-Hop Producer Alive