"and are ok with the admin overhead"
What about the admin latency that will affect everything that they do as well as the huge perf impact that every additional primary site causes?
I agree with Peter -- this is not a good choice.
Is there a reason they can't do everything centrally using a remote desktop session host and VMs located in close proximity to this host. I admit that's not ideal but is much more palatable that 10 primary sites (that makes me shiver).
Do they really have ten different IT groups creating their own OSD content?