But while you're building a new system/subsystem, it doesn't make sense to write unit tests for units of code which have a high likelihood of being deleted 1 month from now due to evolving project requirements.

It's like if you were building a smartphone; it wouldn't make sense to screw all the internal components into place one by one unless you were sure that all the components would end up fitting perfectly together inside the case. While building the prototype, you may decide to move some components around, downsize some components, trim some wires and remove some low-priority components to make room for others. In this case, unit tests are like screws.