Distinction between paging and segmentation?
There are two different address spaces, let's call them logical and physical.  The addresses a programmer thinks about are the logical addresses, the page table translates logical addresses to physical addresses.

As you point out, paging allows you to sparsely map the logical address space to the physical address space.

But the bold sentences in your quote are talking about the sparsity of the logical address space.  The quote is arguing that the valid bit is necessary for the sparsity of the logical address space.