It’s hard to believe this is even a debate. (spoilers - it should be safe:)
At the highest level, this is a discussion about URIs
From the Wikipedia entry for Uniform Resource Identifier:
A generic URI is of the form scheme:[//[user:password@]host[:port]][/]path[?query][#fragment]
The debate is between a scheme safe: and a top level domain of the host .safenet.
Schemes
RFC 2718 Guidlines for new URL schemes is the resource to understand why new schemes may be introduced, as proposed by using safe:
There is a description of schemes as a protocol specifier in section 2.2.2 URL schemes associated with network protocols
Most new URL schemes are associated with network resources that have one or several network protocols that can access them. The ‘ftp’, ‘news’, and ‘http’ schemes are of this nature. For such schemes, the specification should completely describe how URLs are translated into protocol actions in sufficient detail to make the access of the network resource unambiguous.
Section 2.3 Demonstrated utility outlines reasons against using safe: as a scheme:
New URL schemes are expensive things to support. Often they require special code in browsers, proxies, and/or servers. Having a lot of ways to say the same thing needless complicates these programs without adding value to the Internet.
Top Level Domain
The host section of the URI contains the top level domain.
Hosts are explained in RFC 3986 - Uniform Resource Identifier Generic Syntax, particularly in Section 3.2.2 - Host
The host subcomponent of authority is identified by an IP literal encapsulated within square brackets, an IPv4 address in dotted-decimal form, or a registered name.
Hosts are used to locate a piece of information.
The safe network is not a different location for data, it’s a different protocol.
It is abundantly clear at all levels (technical, professional, developers, end-users, software libraries, …) that the scheme safe: is the correct approach and not the top level domain.
If safe is an improved version of the internet, let’s do it right by using safe: and not go backwards by using an unregistered top level domain name based around a centralized DNS system.