Historically speaking, it's because of British snobbery, allegedly. This is how my ASL professor told us it at least.
American Thomas Gallaudet went to the British school for the Deaf hoping to learn BSL, etc. But it was not long after the American Revolution and the British weren't very friendly and wouldn't help him. So he went to France and the French taught him (Old) French Sign Language. FSL became the basis of ASL, along with a number of local influences from Martha's Vineyard sign language (a small locally developed signed language).
Even then, a friend of mine from university who is very hard of hearing and mostly signs told me that on a trip to Britain he met some British Deaf people at a bar and by the end of the night was mostly fluent. There's enough overlap and enough shared experience between Deaf people that one can learn very quickly.
> That said, BSL uses a lot of facial cues, not just hands and arms, to allow for a range expression. Eg puffing out your cheeks to accentuate certain words.
This is 100% common to all Signed languages. Facial cues are huge in ASL. Before class, not joking, I would practice in the mirror to warm myself up. My first ASL prof described it by saying that in English, you could read off each word like a robot, with no inflection or tone- and that would be the same as signing with just your hands.
Sign languages are not based off of spoken languages. Sign languages are languages with their own grammar and vocabulary. They are not a method of encoding spoken language like writing is. The history of Nicaraguan Sign Language is a great example of this. In the 70s the government of Nicaragua set up a school for the deaf focused on teaching its students to fingerspell Spanish. Instead, the students spontaneously created their own sign language.
It’s absolutely bonkers that two fairly different sign languages exist for the same base spoken language.
That said, BSL uses a lot of facial cues, not just hands and arms, to allow for a range expression. Eg puffing out your cheeks to accentuate certain words.