In theory I suppose. But you have to take into account that these APs can potentially be on different subnets, physical networks, talking across ipsec tunnels, dealing with multiple VLANs etc. There's just more overhead. It's easier to push out the info to the APs than to pull from who knows where.

Edit: For example: Say you have two buildings connected via an ipsec tunnel/static route. You have 4 wifi networks on 4 separate VLANs, 2 per building, guest and internal. Generally you'll have an internal wifi controller on an infra VLAN as well.

The wifi VLANs are not allowed to route to the infra VLAN, but infra can route to wifi. Rather than punching holes back allowing the the APs to talk to infra, you push out from infra to the APs.