Handshake does use hierarchy like DNS (you can have any levels of subdomains behind the TLD), except it grants you access to the TLD level at affordable price, that is their main selling point. Whereas today you can only be under a TLD like .com or .us for an affordable price.
The problem they'll have is more and more TLDs are colluding with ICANN's, and Handshake chose to sell "TLDs", plus it is a proof of work blockchain.
Dappy has a .d scoping at the top to avoid collisions, POS blockchain behind it, a co-resolution system (IP addresses and root certificates are always co-resolved), and it allows multi-ownership of names.
Firefox would benefit highly from exploring new ideas, for example the dappy project https://dappy.tech/ which drops the DNS, in favor of a blockchain-based co-resolution mechanism. They are free to resolve dappy names in addition to DNS.
