So instead of torrents, which are shared between each peer without a centralizing server, eD2K needs thoose servers.

The servers just index the files people are sharing. Basically what you are saying is the same as saying that In the torrent world you also need to use a server (the tracker).

The same way you can search the mesh directly in bittorrent, you can use KAD in emule to search for files. No server required.