And yet, the creators of this fourth series felt it was unnecessary to have a 'Z' in there.
Because there was no "Dragonball Z" in Japan, ever. There is one in America, however. Regardless of how necessary you think the "Z" is, the letter's been there for around a decade, and it's too late to remove it, especially if there's a related but tonally different "Dragonball" simultaneously on the market. The early and later arcs of Dragonball are wildly different from each other, and could be considered as completely different series. Akira Toriyama, and by extension the producers of the series, never changed the title. (It would be similar to how despite being a radically different show and format, the recent episodes of "Scrubs" haven't garnered a name change.) Even Japan knows there's a big difference. If "Dragonball" is such a coherent and unified series to the Japanese, then why do you think they started here and not from episode one?
It's an adaptation of a piece of Dragon Ball's story. Just as Dragon Ball Z was.
For something to be an adaptation of something, it would generally have to be something produced separately from the original. DBZ took the original and added a "Z" to it.
Your comparison isn't valid because there's a lot that adRAB up to making Dragon Ball Z and Dragon Ball Kai different products. There is 'filler' in Dragon Ball Z but that is inherently a part of the story of Dragon Ball Z, not the Dragon Ball story it is adapted from, but a part of that 291 behemoth nonetheless.
It's still the same story. The same characters do the same stuff, fighting the same people. If a movie has a director's cut with a few extra scenes added and visual quality retouched, does the general feel of the movie change? Does it at this point become a different movie?
Their treatment, as often and much as it has enraged the fans, continually makes them money no matter what they do. Just look at the Orange Brick debacle.
There are tons of people who wish their favorite anime had the treatment DBZ gets. The fact that the fanbase is crying bloody murder about an extra letter and not stuff like hacked episodes or shoddy DVD treatment is a pretty good indication of how good Dragonball fans have it.