Smart speaker sales continue to grow. The smart assistants attached to these speakers continue to improve.Apple doesnt need to prove anything. The HomePod is a great speaker and people who want it and like it will buy it if they see the value in it. People who are fine with speakers that collect their data and sound like oversized cell phone speakers can keep their Amazon echo and google home.
Obviously Apple understands this and that is why they've introduced the HomePod Mini. By having a lower cost option, it will open the opportunity for more customers who are already in the Apple ecosystem the option of adding a smart speaker. Without that option, and with the growth in smart speaker sales, Apple runs the risk of having some of their customers slip away from the ecosystem.
One of the reasons why Apple has been so successful in retaining their customers is by giving them more options to be plugged into Apple's devices and services. It's called a "walled garden" for a reason. The HomePod Mini is an important piece of that.
What Apple has to "prove" with the HomePod Mini is that it is good enough for ecosystem denizens. The Mini doesn't have to be as good as or better than the alternatives... just good enough to keep customers in the fold.
The HomePod line is not a general purpose smart speaker option, but is smart speaker solution for those in the Apple ecosystem. Those are two different things.