it doesn't work well for describing how the writing system of modern Hindi works.
Sure it does. Consonants always have the vowel a
in Hindi, except when other vowel diacritics are added, or the virama is used (most often expressed with the use of conjuncts). The exception is at the end of words where the final -a
is usually not pronounced, but it was in Sanskrit.
This isn't true, however for some languages like Bengali, where the inherent vowel is o
. But this is due to a phonological shift, not the inherent design of the script.