The computer was tasked with creating an opponent that could defeat Data. Doing so required analyzing Data to assess what would be needed to fulfill that request. And the most complete source for that info would be the transporter, which has broken Data down at a molecular level and rebuilt him numerous times. And using that info, the computer imitates Data's own neural net as a baseline, then grafts a holo character on top of it. That these the things are compatible and can be so easily integrated is also demonstrated in A Fistful of Datas.

The EMH had to be built from scratch, as there wasn't a way to essentially steal Soong's life's work as a shortcut.