no team collaboration gain with the open plan, that's a myth. Mainly it causes increased use of sick time and increased turnover.
Having to compete with others to move your station to a community temporary private spot is not privacy at all, but justs wastes everyone's time.
If it costs more to have a private office, fine. Pass that along to employees if they are interested in one - lower their pay. Then when you realize they are more productive that way, apologize and restore it.
You have a chance to do some real good in the world. Don't blow it.
Oh, and make sure everyone has plenty of desk space. Absolutely frustrating not to.