Hi,
it looks to me that the reason for 'IDE Controller' missing may be actually in the box.ovf file, ~/.vagrant.d/boxes/centos-VAGRANTSLASH-7/1610.01/virtualbox/box.ovf.
Comparing the box.ovf file from
puppetlabs/centos-7.2-64-puppet to centos/7 I see many namespaces are missing in the Envelope of the latter.
So I took the box.ovf from 1.0.1 puppetlabs/centos-7.2-64-puppet copied it over centos/7, and modified it (attached) to match the 1610.01 centos/7 one.
This consisted of replacing the vmdk name and uuids (diff vs. the original puppetlabs ovf attached), and 'IDE Controller' is again available. I'm on Ubuntu 14.04:
$ vagrant --version
Vagrant 1.9.0
$ vboxmanage --version
5.1.10r112026
All this may be still due to a mystery about 'IDE Controller' that we don't understand, and I may just be lucky, but it is worth trying on more platforms.
Another hint that something may be wrong with centos/7 box.ovf is the fact that the boot order reported by the original centos/7 box,
and the Vagrantfile after the "workaround" of replacing 'IDE Controller' -> 'IDE' does not correspond to the boot order in box.ovf:
vboxmanage showvminfo --machinereadable <uuid> | grep 'boot.='
boot1="floppy"
boot2="dvd"
boot3="disk"
boot4="none"