The handshake team itself has never used language like "overthrow", and have carefully designed the system to work with DNS, not necessarily replace it. From their FAQ:
> Does Handshake replace DNS?
No. Handshake is meant to replace the root zone file, not DNS. Browsing the web with human readable names is what Internet users have gotten acclimated to. Our solution allows for a seamless transition between a centralized name root zone file controlled by private parties to a decentralized root zone file controlled by actual Internet users. The Handshake blockchain itself is essentially one big distributed zone file in which anyone has the right to add an entry in.
> Does Handshake replace DNS?
No. Handshake is meant to replace the root zone file, not DNS. Browsing the web with human readable names is what Internet users have gotten acclimated to. Our solution allows for a seamless transition between a centralized name root zone file controlled by private parties to a decentralized root zone file controlled by actual Internet users. The Handshake blockchain itself is essentially one big distributed zone file in which anyone has the right to add an entry in.
https://handshake.org/faq/