Search is, by it's nature, something which "must" be centralized. We can't all run our own search engines- it'd take too much data & compute to index & rank the internet. So there's a bunch of managed services, like Google Search, like Duck Duck Go.
I don't think there are any notable products that compete with Google Home. Google Home is a very big tent operation, with a vast array of devices from all manners of companies under it. Trying to imagine where we'd start at building products against that is almost unimaginable.
Instead, look to protocols. What protocols might be created that could allow communities & ecosystems to start up? Chromecast itself was built on an open protocol, DIAL[1], spearheaded by Netflix, for taking over screens. Today, the web has a very successful protocol the Presentation API[2], that allows for sending content to screens/speakers about us. Currently the proprietary Chromecast protocol is the primary & perhaps only implementation of this. The same Secondary Screen Working Group has however shipped a draft[3]- a year ago- of Open Screen Protocol, an service providing interface for devices to expose & consumers to push content to the devices from, which is an open, intercompatible way of making the Presentation API happen.
[1] https://en.wikipedia.org/wiki/Discovery_and_Launch
[2] https://w3c.github.io/presentation-api/
[3] https://www.w3.org/blog/news/archives/8973