It's been many years since I studied Sanskrit (two courses in college, plus a course surveying Indo-European languages). And it is certainly a wonderful and poetic language (we read the Nala story from the Mahabharata in the first course and some of the vedas from the Rig Veda in the second course). But although my coursework is quite ancient by now, I don't believe the linguistic principles have changed. Sanskrit is not the mother (or father) of all Indo-European tongues. That would be what we now call proto-Indo-European, which (at least this is what I was taught) began somewhere in the Caucasus region and spread throughout Europe and India, developing into the various Indo-European languages that we now have records of--there are no written texts in proto-Indo-European. Sanskrit is more like a sibling than a parent (though it's certainly an older sibling).

I think that you're quite accurate that Sanskrit is "logical and rule-based." That's because what's called "classical Sanskrit" was standardized as a written language. Apparently there's some debate as to whether Sanskrit was ever a vernacular language, except among the educated class (a little like the way educated Europeans in the middle ages spoke Latin, though it was never anyone's first language at that time). Every vernacular language has some irregularities (in English, for example, the past tense of "dive" is "dived" but the past tense of "drive" is "drove," so we call "drive" an irregular verb). Classical Sanskrit grammarians "regularized" the language by eliminating any inflection that didn't follow the overall patterns of the language. That may be the reason it's such an appropriate language for AI (but I'm REALLY out of my depth on that issue). This sort of regularity means that once you grasp the overall shape of the grammar and learn the characters of the syllabary (the Devanagari is not an alphabet; each character represents a syllable) , it's not particularly difficult (English is a much harder language for anyone for whom it's not the first language). I would encourage anyone who wants to learn this beautiful form of expression to find a good (and patient) teacher and begin the exploration. I wish I had kept up what I learned. Thank you for your passionate introduction and elaboration.