Except the rest of your arguments fall apart if your point is just "Sanskrit and English shared a common ancestor thousands of years ago and English (and some actual ancestor languages to English) pulled in some Sanskrit loan words". As other commenters mentioned, lots of languages (and languages with long and robust literary traditions) fit this bill, so from an English speaker's perspective there is nothing special about studying Sanskrit. If anything there are a host of more direct ancestors.

The perspective in your post is rationalistic and not empiricist. There was no theorematic argument intending to prove the importance of Sanskrit (and Greek, and Latin) for the understanding of English based on historical notions: it was a witnessing of the importance of Sanskrit (and Greek, and Latin) for the understanding of English based on experience.