I have a cheap Xiaomi phone and it runs the same apps everyone else does.
My guess is that the expensive phones are bought primarily for their cameras. I'm not big into photography but I can see how that makes a stronger argument for the likes of the iPhone X and Note 8 etc.
With that said though, I've been with Android since the G1 (literally all of the Nexus lines), and few cheap phones compare to the high end phones for me.
My best phone of all time? The Nexus 4.. or was it 5... I honestly can't remember now. It was one of these $200 phone. It felt cheap as hell, but it was a very nice compromise on features vs price. Yet, that's going back to what I was saying above. Despite me loving that phone, and it being an amazing phone for $200, it was still a compromise of quality. If you show me a phone that has the OS and build feel of my Pixel 1 XL, I'd happily buy it. However, I've not ever seen this. Same goes for my Macbook Pro. It's far from perfect, and definitely feels overpriced, but the OS and Hardware combo has no competition from my perspective. Unfortunately.
So back to your original question, I definitely don't do anything with the phone to inherently justify the price.
For one, some might make so much, that it's not "super expensive" to them -- just a phone, and they buy whatever they like, whenever they like.
Second, some might use it as a status signal that they have such a phone. Which might not be as effective as a house or an expensive car, but combined with other such stuff, works wonders socially compared to not having it. This depends on your social aspirations of course (e.g. caring to play this game, climb some social ladder, for small "status" differences etc).
Others are interested in gadgets, and can save and sacrificice other stuff to have the latest phone/PC etc, even if they don't make as much money.
Others are hobbyists (or semi/pros) and use them for their camera, video, music creation, drawing, etc capabilities.
For others yet it's a fashion accessory. The buy expensive phones for the same reason they wouldn't want to be seen with old cheapo sneakers (this is similar to the "social status" thing).
I'll spend more on coffee than I will on an "expensive" phone during the same time.
How is that stupid? It's not like a brain surgeon who just gets what's the best out there (or considered top) is in any way stupid because they're not a tech-geek to care to do a full "market review" on their own...