It's not your/your co-worker's desk. That's in your own home. This is the company desk they lend to your use. If you are not permitted to lock it, you are not permitted to lock it, and anything personal you keep there is at your own risk. I think it's a strange way of going about things, but not my place of business. Personally find it kind of dehumanizing to treat employees like children or criminals.
I am required, as a part of my job, to check everyone's desk, credenza, printer, computer, files, etc. for security. I am also required to keep spare keys for all locks, with the firm understanding that your desk is for your use, but may be opened or examined at any time. We have plenty of people with personal stuff up for grabs (snacks, cookies) and plenty of company stuff locked up. We have multiple people using various workstations as needed. Depends on the office environment.
In the spirit of camaraderie I'd tell your cube-mate about the extent of the rifling, as a heads up, and leave it at that. They can deal as they see fit. And I'd not keep anything in MY desk that I didn't want stolen!