Let me clarify my position.
In previous editions of the game, you have various levels of at-will weapon damage for the classes. Some classes were great at it, some weren't that great. 5e maintains that sort of spectrum.
In previous editions the way this was brought about differed by edition. In AD&D only certain classes got multiple attacks. Others may not have had their melee weapon attacks scale at all.
In 3e, everyone had multiple attacks, and where on the spectrum your class was expected to fall determined how many of those you got and how fast you got them.
In 5e, the way in which this scaling happens differs by class, and sometimes by options within the class. The primary weapon users get Extra Attack, and often get something else to go along with it. Other classes might get Extra Attack without anything else to help it out, or a lesser option such as Divine Strike. And the classes that aren't traditionally great with melee weapon scaling get green-flame blade and booming blade as options in case they do want some melee weapon scaling.
Druid, traditionally somewhere in the middle to lower-middle on that spectrum is lacking a damage scaling option in 5e. It is singled out in that situation. (Sorcerer, Wizard, and Lore Bard were also lacking an option until SCAG, which gave them an option.)
The reason I find this particular lack annoying, beyond mechanical reasons, is that a druid that wields a staff (or scimitar) is one of the most iconic images of early D&D druids. When I say, "wields a staff" I don't mean someone who goes into battle in a whirling staff frenzy, using all sorts of spells to boost his staff damage. No, most of the time druids have traditionally stood back and used their spell slots. But when they do want to make a weapon attack, it should have (at least the option of) damage scaling like every other class, with the weapons that fit the image.
It's not a weapon using melee druid build. That's rarely been a thing in D&D history (I almost said "never" but I'm sure someone has done it.) It's the option to have their melee weapon damage scale when they are using it, so they are not uniquely denied that scaling damage.
Divine Strike, and Extra Attack and/or green-flame blade or booming blade.
You're right, druids don't need Extra Attack. They probably should have been designed with something like Divine Strike, because they should be on the same part of the spectrum as clerics for melee weapon damage.