If teaching Indian ethos and values is the objective of the Central Government and a certain Judge, why not start with Thirukkural? It is Indian but has universal appeal; it is ancient but has contemporary relevance; it is simple enough for kids but deep enough for scholars; for the most part, it is secular and has largely been accepted by all religions; it should already be available in most of the official Indian languages and it has already been tested at all academic levels for many years.
But of course, the original is not in Sanskrit. And though Hindus claim it to be their own, so do others, especially Jains. Do these make it any less a candidate for being considered a quintessential work on Indian culture and values?
Or why not Dhammapada? It is beautiful. It is Buddhist but many portions will be acceptable to almost everybody.
I personally don’t have any objections to having Gita and Mahabharata ALso at school (in addition to selections from Bible, Koran and other important religious works), as long as age-appropriate sections are selected and are presented without any indoctrinatory motives, willful distortions and jingoistic reinterpretations. I am actually surprised that schools don’t have them already. In Tamilnadu, where the more socially progressive (pseudo or otherwise) Dravidian parties, branched from an atheistic movement, have been in power for 47 years, we have been reading Bhakthi literature and Kamba Ramayana at schools all along, along with representative works from other religious texts in Tamil.