Is there a special reason for why future perfect continuous is used as this English translation of буду сидеть?
Because сиде́ть is a imperfective verb that emphasises a process.
So how would you say, "I will sit on this couch."
I think you should use the imperfective 'посидеть" if you want to emphasize the action of 'sitting down' rather that the process
"Посидеть" means something like "to sit for a while". The action of sitting down is expressed with the verb "сесть". "I will sit on this couch" would be "я сяду на этот диван".
They want you to focuse on the action of sitting rather than the result of being seated. That is why you use imperfective future with буду
"я буду садиться на этот диван" would take accusative as it involves motion? Can a native speaker confirm/contradict?
Yes, you're right about the accusative.
What's wrong with translating диван with sofa?
"Я буду сидеть" и "Я сяду на этот диван" - почувствуйте разницу.
the phrase in english sounds really awkward, I can't imagine somebody using it. Is it expressing a conviction that he will be able to sit in the sofa, like a man saying I will be sitting on that throne?
it has tonnes of uses in English you just haven't given it enough thought.
For example you are directing a film. " You will be standing over there when Masha climaxes, and I'm going to be sitting on the sofa"
I could give you a hundred other examples
Диван is like a sofa (cf: french divan)
пока ты смотришь на одежду