Idk about the exact reasoning/history behind it, but dedicated animal companions in 5e are much more of a Ranger thing, through their Beast Master subclass. Along with a less-powerful Familiar for Wizards and certain Warlocks.
Druids do have a Circle that focuses on their connection to "spirits of nature," the Circle of the Shepherd. They get an AoE spirit effect that can do different things depending on the animal spirit it represents, and they also get more powerful beasts or fey Summons.
I found this tweet by designer Jeremy Crafword:
https://twitter.com/jeremyecrawford/status/943561637713215488?lang=en
