I too had lessons bareback. But only in my 2nd year of riding. The teacher explained that riding bareback and thus improving my balance would reduce the likelihood of my falling off. I also rode a lot with no stirrups. At the end of each lesson, like you I was left to myself on the horse with no particular instructions about how to steer or how to control the speed.
At my first RS, I was simply told to look where I wanted to go and the horse would go in that direction. I would do a lot of closing my eyes and praying. What adult beginners really need, since we are human, is a verbal explanation of what we are signalling to the horse.
More advanced riders can indeed steer the horse by just looking in the direction they want to go. But beginners benefit from a basic introduction to conventional aids using their hands and legs. Start with A B C before you attempt to appreciate literature.
I always wore a body protector when riding bareback and the horse was in a neck strap too. Eventually I learned to trot bareback and how to balance myself bareback in trot on both reins (going in both directions round the circle or round the school)
Some teachers believe students need to be able to canter bareback or even with no stirrups, but I started riding in old age and never did this. I think the idea is that if a new rider loses a stirrup when cantering, they will be able to continue riding, can control the horse, balance on it and wont fall off. I have never lost a stirrup when cantering so with me the situation didnt arise.
But this shows that every rider and every horse is different.
As for putting on and taking off the tack. I think learning how to do that is important too because one is dealing safely with the horse and doing things to it from the ground. Horses can kick and bite. It sometimes feels as if one is making no progresss, But apart from untacking the pony and putting on a rug, I did none of this till my 2nd year of riding. It was years before I put on a bridle.
My husband never learned how to tack up and untack a horse. On traditional UK yards, a groom would prepare the horse for a genteman to ride. At some point my OH was asked whether he wanted to learn how to do this himself and he said that he didnt.