Sophie, yes, you read correctly that's why I was so confused by the product. The cast was light but would not budge 🤷
No I've always worn my hair curly (or wavy really) Pupsie, and I've always had the standard wavy cut (layers at the front from the chin down) unless it was short (thanks to crap hairdressers). I've had one curl cut specialist cut and it was really bad. It was cut in the round sort of, I think that's the Deva curl technique and with a great amount of product it looked 3a/3b but it dropped pretty much within an hour to my normal looser pattern. It didn't really bother me until I washed and air dried, the amount of funk in my hair bothered me more. I had to blow dry it from then on until it could be cut into my preferred cut (at the right length, this seems to be my contention with hairdressers, they think cutting is the same as with straight hair, so they take more off and it's a huge amount once it's dry just from the bounce of the waves). It used to be pretty self sufficient but medication and hairloss has upset the balance. I'm really lazy with my hair and ideally I'd get back to my usual routine of being able to just wash condition and be done with it. I also have a preference for messy French girl hair so I'm not aiming for perfect curls either.
Soft probably is a bit of the grass is greener thing if you're on the coarser side. My hair is quite smooth, that's not something I have to work for all that much but soft usually means a bit limp and lacking volume on the upper third of my head for me as my hair doesn't curl from the root (another wavy thing as I understand it). I need a bit of texture that's not frizz basically.
I'm not sure about the need to squish with a thermal cap, I think the heat gets the cuticles to open up or the hair swells (one or the other) to allow for better penetration, the squishing method seems to be a less efficient mechanical version of it.
Pupsie I think there's something similar to that band called the zazzi band or something like that, without the claw thing but same idea.