Amazon Prime subscriber here.
I haven't bought toilet paper on Amazon. Costco's still got my TP dollar. I think it's $15.99 or $17.99 there for a "cube" and it looks like the equivalent is about $20 on Amazon. Maybe I'm misremembering/looking at the wrong thing.
Anyway, yes you can use your Prime account on phones/kindle/tablet. I use mine on my phone for Amazon Music. Their video selection is decent (but the interface is awful) with a few gems like The Man In The High Castle.
So, other than toilet paper, what is the benefit of prime?
For us, the real benefit is having to go to any stores for only fresh groceries, and able to buy nearly everything else online, mostly on Amazon. Us damn millennials hate going to the store, and Amazon is capitalizing on that. Recent random purchases: books, computer parts, dog treats, shelf-stable groceries, photography accessories, phone cases, Dremel sanding bands, dog shampoo, kombucha scoby. No store has all of those things, and certainly none would involve only a few minutes of my time.
Free (>$35) same-day shipping (if ordered before noon) is available in my area too, which is turning out to be outrageously convenient. My wifi router died a while back on a
Sunday morning, and we were going to be gone all day. I placed the order for a new one at 7am before we left, and it was waiting for us when we got home at 4pm. One time, I needed tamarind paste for a recipe, ordered it (along with other stuff to bump it over $35) at work at 11am, and it was waiting at home for me when I arrived. No need to dig through a grocery store to find it. GF texts me one morning saying one of the dogs might have fleas and we need some specialized medicated shampoo ASAP. Arrived within a few hours. It's great.
Amazon keeps giving me fewer reasons to go to the store, even in "a pinch." Once Amazon nails down fresh groceries (it'll happen), I'll hardly ever need to go anywhere to buy anything.
If there's a shipping snafu (very rare), they'll usually extend your Prime membership out a month if you bitch. One time when I complained about that (something arriving a day late), they instead let me keep the item and refunded me ($40). All this was done through the online form, no phone call needed.
We order stuff from amazon fairly often - 16 separate orders this year.
Oof, do you even lift bro?

Kidding aside, we (household of two) share our account with three people that each order stuff occasionally, "only" about 100 of those orders are truly ours. And with no order minimum, some are small <$10 things.