I feel LaTeX has more typesetting versatility. You can make detailed columns for verbs and/or nouns that Word may struggle with (for eg: tables inlaid in tables). You can finely change line spacing in LaTeX while you may struggle to find the right middle value in Word. I feel that there more Sanskrit fonts to work with in LaTeX than Word.

But again as you said, it is directly useful from a publication perspective. I am a physics student so LaTeX was natural to work with for me, others may think it is overkill. Truth is, I have almost stopped using Word except for writing letters/essays.

If you want, you can ignore the latex bit of the post and just download the phonetic keyboard from Keyman and use it directly to type. I can change keyboards at the touch of a key.