My office is in the process of moving to a new location, and I cant imagine the chaos if we were asked to move our own stuff.
Instead it's very organised.
There are about 500 of us moving. The company ordered loads of boxes. We fill as many as them as we need with our files, folders, papers etc, seal and label them with our seat location in the new building.
The removal team are currently moving boxes as they become available, and when we arrive at the office next week, the plan is that all our boxes shall be waiting at our desks.
All PCs/phones/bins/coat-hangers/cupboards etc are labeled, and shall be shipped aswell.
The only thing we have to carry by hand are our laptops.
There is no way I'd accept transporting all my own stuff under my own steam - for a start I cant even lift my monitor, never mind a large box full of files. And the company cant assume that everyone has access to a car (for example I dont, and wouldnt be prepared to pay for a moving van for my stuff).
I think the orginal poster's company if being unreasonable, penny-pinching, and shall only loose out in the long run.