I can't say I have a definitive answer but from what I've heard it was a combination of money and timing. Back in the 1970s-80s, Toho definitely licensed the characters separately, which is why only Godzilla was used for the Marvel comics series, the Hanna-Barbera cartoon, and the occasional US toy or game. Aurora did license Rodan and King Ghidorah for model kits, and Mattel made a Rodan figure to go with their Shogun Warrors Godzilla, but those were rare exceptions.
Dark Horse got the Godzilla comic book rights in 1986 or 87. At that time they were a small black and white publisher so my guess is they didn't want to spend a ton of money licensing a bunch of monsters (or even the key ones, which would probably be the most expensive).
In the mid-1990s Toho finally opened up and began offering several monsters as part of their licensing deals. That's when we started getting the more extensive product lines like Trendmasters toys, the Random House Books, Bandai Creation, and the Atari games. My guess is Dark Horse could now renew or renegotiate for a similar deal with Toho if they were so inclined.
On a related note, when I worked on GODZILLA: THE SERIES the producers told me they had permission from Toho to create new versions of the classic monsters. But if they had designed (for example) a new Mothra it would have to be sent to Toho for several levels of approvals, then changes would have to be made based on Toho's requests, and then the revised versions would have to go through approvals again. Since everyone was working under deadlines the producers decided to skip all those headaches and just create new monsters for the show.