I'm not sure if the exact amount of $7.85 is necessary (there's definitely a decent profit margin there), but charging a registry fee is definitely necessary. There are a lot of costs that go into running a registry. This is my understanding of what running a gTLD registry looks like today (I run a registrar, so I'm on the other side of the picture, so I may be missing a few things).

$185,000 application fee (+50k if a technical review is required)

$6,250 fee per quarter

$0.25 per transaction (registration, renewal, or transfer)

More fees I'm forgetting

You also must run/maintain a bunch of other programs/services like: (this is the bulk of the cost of running a registry) shared registration system (SRS) that implements EPP (used by registrars to register/update domains), whois service, abuse prevention/mitigation, rights protection, dns services, zone file distribution, data escrow, DNSSEC, etc...