This is just a guess, but reading RFC 819 (https://tools.ietf.org/rfc/rfc819.txt), which transitioned ARPANET to a hierarchical naming scheme and also predates DNS, the little-endian notation might be a simple artifact of ARPANET's e-mail addressing. E-mail addressing was already user@host, which is basically little-endian. It would be consistent to extend it like user@host.site.network. JANET also used @ notation, but used big-endian notation for the domain, which seems inconsistent, at least from a user's perspective.

Wikipedia says JANET's e-mail addressing notation was defined by the "Grey Book", and this Usenet thread, http://neil.franklin.ch/Usenet/alt.folklore.computers/200209..., says the Grey Book domain notation comes from the Network Independent File Transfer Protocol (NIFTP aka "Blue Book", which was a different protocol from ARPANET's RFC 354 FTP). This 1990 JANET<->ARPANET e-mail gateway document, http://dotat.at/tmp/JANET-Mail-Gateways.pdf, says that JANET e-mail was transferred using NIFTP, so it would make sense that the domain part of the e-mail address would use NIFTP rules. Both above sources say (explicitly or impliedly) that JANET generally, and NIFTP specifically, were based on X.25, and X.25 uses big-endian addressing.

So on JANET the hierarchical naming scheme predated the e-mail addressing scheme[1], whereas on ARPANET the reverse is true. Both formats make sense as path dependent outcomes.

[1] Presumably JANET still adopted user@ because the message format was based on RFC 822, according to that gateway document above, but it was still worth partially deviating from RFC 822, which explicitly defines little-endian domain syntax, because of JANET's pre-existing host addressing scheme.