First, I appreciate this emphasis on shapes of the hands, which is not something you see emphasized in modern dance, and also not in any classical Western dances I am aware of. Yet the hands are very dextrous, so why not? In our mind-map they probably take up a lot of space.
Related, I find it enjoyable how some forms that westerners think of as being for "shadow puppets" or children's games have been elevated here to respected parts of an art form. It's great.
And even if some parts are intentionally silly, or humorous -- well, great! Comedy is necessary.
Second, it's an example of a taxonomy or ontology, which is something I have been thinking a lot about these days. Very clearly there is a continuous space of hand poses, but certain discrete points in that space have been selected to convey meaning.
Finally, it's an escape from the current Culture, which I find exhausting. Yes, please do give me thoughts from a time and place where other thoughts were thought.
Like, imagine the mental state that is required to invent this taxonomy. You'll get some of that by thinking about it. It's like a breath of fresh air.
Here is my take: Mudras are an elaborate form of encoded symbolism with a long history in culture that influences a large part of the world. People trained in classical Indian dance will be able to decode a story based on these gestures, whereas someone who doesn't know much about it won't get the meaning. If you think about it like that, it's quite similar to code. At the end of the day, computer code is also just symbolism - so we as practitioners of this particular kind of symbolism can always learn about other forms of symbolism to improve our craft.