Our kid is cautious of height

I wouldn't place it that our girl is acrophobia (fear of height) because she would dare taking a few steps up the slide and no problem with sliding down afterwards. That is a great accomplishment and a no-no for strictly defined acrophobes.
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You see, as she is our first child, we tend to go overboard in protecting her and we inevitably imbued in her certain characteristics, and unfortunately being overly cautious is one of them.
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We are fortunate that she is not a rebellious and negligent kid. That is why she never had any serious boo-boo (injury). However, when a person is unfamiliar with pain, they tend to be  infrequent at attracting pain by being over-cautious.
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It is not healthy to bring up kids to be over-cautious and less daring to try. For her, she was late at picking up many motor skills, e.g. holding on to hand rail with climbing. Such coordination with the hands and legs seemed so challenging to her! I felt bad and sad seeing her immobilised with the fear of falling and deprived of carefree fun.
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Now at almost 3 yo and after several months going to the neighbourhood playground, she had demonstrated great improvements. By encouraging her to try, she had developed several basic motor skills. Her depth perception (part of child's eye development) no longer served as a weakness (inducing acrophobia) but as a needed attribute to scale height and physically interact with her surroundings (e.g. how acrobats catches horizontal bar in midair based on depth perception).
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She had several bruises but that is part of learning to rise up after each fall. As parent, I can only try to minimize the impact and nurse any wounds.
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Note
Our kid climbed up the slide and on the last few steps to the top, she crawled (on four limbs) up to the platform. Once there, she laid down on her belly and slithered (with her belly constantly touching the support/platform) to the edge where the sliding board was located. There, she inched herself up and ended up in a sitting position. Then,  I would give her word of encouragement, two thumbs up and counted to three before she slide down. Sliding down wasn't a problem.
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After several visits, she started from crawl to walking-like-duck, and finally experimented with walking upright. I was excited to see such transformation. I'm waiting for the next phase in which she will run up and zoom down the slide in split seconds. Haha.
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Just to share.