I don't know of any applications that require RFC1918 addresses to be deployed. (Clearly, this is not to say there are none.)
There are a number of good and reasonable uses for RFC1918 addresses. Just assume a individual/business/corporate LAN with client/server applications and statically configured ip numbering. RFC1918 addresses are perfect. NAT allows this network to be connected through any provider(s) to the Internet. There is no risk of collision of the internal address with publically routed addresses. To do without RFC1918 type address space it expect to a. Obtain unique, permanent address space for personal/business/corporate use b. Receive this unique, permanent address space at no cost c. Have this unique address space routed via any provider of my choosing Adi