I tend to agree. I don't remember druids even being able to shapeshift in 1E/2E, so shapeshifting was never an important part of the druid concept to me.
On the other hand, shapeshifting is a choice niche in 5E -- especially compared to the overcrowded pool of full-casters.
In 1e they didn't get it until 7th level...same, I think, in 2e. The "shapeshifting druid" is definitely something WotC did and reinforced with each of their editions.
I also believe the popularity it being a druid concept "archetype" (and I use the term loosely) has something to do with the "druid" class in the World of Warcraft MMO having some kind of shapeshifting ability. Hence, as 3 turned to 3.5 to 4e and now in 5e, the idea that a druid MUST shapeshift and it's the kewlest thing they should be able to do (now in 5e) from 2nd level on has only continued to tighten its grip.
But I must concur with the prevailing sentiment in this thread thus far. Shapeshifting, arguably a shamanistic ability and druid's could definitely fall into that type of character, it is FAR from the dominant historic or mythological abilities of the celtic priest Druids.
Druids should be spell-casters, first and foremost. I would even pose that through their magic, animal companions (in the sense of utility: scouting for you, tracking for you, communicating messages to other druids, etc... NOT the "I'm a Summonuh who poofs animals into existence to fight and die for me! That's a totally normal drooid!" way) would come in second place. Shapeshifting, sure is a flavorful ability...and fits well in with the whole "connection to/one with nature" thing. But it certainly shouldn't be from 2nd level on and definitely shouldn't be the PRIMARY signature ability.
Nature Magic is the druid signature ability. Casting spells that do things that Clerics don't/can't and Wizards don't/can't.