There are two major use cases as I see them, and both are buoyed by the fact that these days, speech recognition by devices such as the Echo or Google Home is actually quite impressively good -- it can pretty consistently understand your words from across the room, while it's playing music, for example.
The first case is the "want" factor that others have mentioned on this thread. It's less that I "need" an Echo in my home, and more that it makes certain activities easier: I can get measurement conversions, set timers, and pause my movie while my hands are occupied cooking in the kitchen; I can get the weather forecast while putting on my shoes on the way out; and now, I can also answer calls and send/receive messages while my hands are occupied. It's less that I couldn't do that with my phone or computer and more that Echo-like devices make this more convenient.
The second case involves the fact that there is a comparatively small, but still significant portion of the population that cannot effectively use touch devices to do the things that the rest of us can easily do with our phones. The people who "need" this kind of device the most, in my opinion, are those suffering from paralysis causing them to be unable to use their hands or fingers with enough dexterity to operate a touch screen, or unable to use them at all. These devices are real life-changers for this group, since they can now control lights, their television and other entertainment options, and talk to their loved ones -- all activities that were difficult, expensive (requiring specialized devices), or impossible before.
In addition to this first group, there are also those who often have difficulty figuring out how to use computer/touch screen technology, even though they are physically able to -- the elderly are probably the first example that comes to mind. It's much, much easier to just set up an Echo Show and be able to "drop in" on your grandmother and chat, than it is to get her set up with an iPhone or a computer and teach her how to Skype or text.
So all in all, most people will get this for the "cool" factor and because it makes their lives a little easier, but some people will gain a huge benefit from it.