There are actually a lot of Godzilla movies where Godzilla has relatively little screen time or doesn't really show up until the final act, although admittedly this one is fairly low on the list of Godzilla screen times.
This blog has some graphs comparing Godzilla's appearances in all the films (excluding the Emmerich/Devlin film, of course, since the actual Godzilla does not appear therein). In terms of Godzilla's absolute screen time, the 2014 film comes in 20th out of 29 -- but as a percentage of total runtime, it comes in second-last, only beating out
Invasion of Astro Monster. There's only one film where Godzilla's first full appearance comes later (the previous one,
Final Wars), but six where it was later as a percentage of total runtime. (The most extreme case is
Terror of Mechagodzilla, where Godzilla doesn't even make a tease appearance until 58% of the way into the film.) And the '14 film does come last in the duration of the Godzilla fights/rampages, though it's not far behind the '54 original and the '84 reboot.
Anyway, I don't mind Godzilla's limited screen time in this one. It's a monster movie, after all, and generally those are undermined if you show the monster too much. What we did get was really impressive visually, especially in 3D. The problem was simply that the human stuff going on between Godzilla scenes wasn't as interesting as it could've been. (Really, they should've kept Bryan Cranston as the hero for the whole film.)
My main problem with Godzilla himself is that he was a bit too domesticated, too much of a hero. In the Japanese films, he's generally only been heroic in the cheesier, sillier installments of the series. Otherwise, he's either been a villain or an antihero, a force of nature that can save us from even more malevolent beasts, but who's still quite dangerous to humanity.