I can give some background information of why it might have happened. A state-by-state answer is however beyond me.
Firstly, it is important to understand that alphabets are rarely a perfect match for a language. Alphabets provide symbols for the phonemes that make up a language. However, each language uses different phonemes. The closest you can get to a universal alphabet is the International Phonetic Alphabet, devised by phoneticists.
International Phonetic Alphabet - Wikipedia
This has over 100 characters and more than 50 modifiers, and so is unsuited for general use. Instead, languages choose a more useful alphabet that is small, but can cover most of the phonemes in their language.
The first alphabet was devised in southern Canaan in the 2nd Millennium BC, and propagated by the Phoenicians. This alphabet contained only consonants, which works for the semitic languages spoken in that region as the vowels are easily inferred. When the Greeks took up the alphabet in the 8th century BC, they added in separate letters to represent vowels, as those particular sounds were important in their language. As the alphabet diffused into Europe, some adjustments were made to suit the local languages. For the Slavs, the Greek alphabet was changed in Cyrillic; for Western Europe, the Latin alphabet was devised. The match of alphabet to language was rarely perfect. Sometimes new letters were added, like the German β character for ‘ss’, or modifiers such as the Spanish ň. In English, we used double characters such as ‘sh’ and ‘th’ to represent phonemes that the Latin alphabet did not cover.
The Asian alphabets derived not from Greek, but from the original Phoenician alphabet as it travelled east. Like Phoenician, Hebrew and Arabic are still written without consonants when in their pure form (although later scribes devised ways of adding vowels). Like European languages, the languages in the Indian subcontinent needed vowels, so they were added but in a different way to the simple characters used by the Greeks. Instead, a semi-alphabetical scheme was used. Consonants carried an implicit following vowel, normally a short a; a diacritical sign could be used to remove that vowel. Additional vowel characters were used for words that start with a vowel, with different diacritical characters used to flag a vowel other than the default following a consonant. Ligature characters were used where two consonants are not separated by a vowel. All this resulted in many more characters; Sanskrit for example had 48.
The Brahmi script of India from the 3rd century BC was the original South Asian script, probably derived from the Semitic alphabets, and the other Indian and South-East Asian alphabets derived from this. (East Asian languages do not of course use an alphabet.) I do not know the details, but I suspect the slightly awkward nature of Brahmi led each Indian state to attempt to improve on it, taking into account the phonemes in their own language. No doubt nationalism may also have had a part to play in the desire to make changes.
Brahmi script - Wikipedia
A good book is read is “The World’s Writing Systems”, by Peter Daniels and William Bright.
Incidentally, the often poor match between alphabets and languages have sometimes caused significant problems, notable in Central Asia. Turkey changed from the Arabic script to Latin-based in 1928, as part of the Kemal Ataturk reforms. This sort of change has major consequences: younger people can no longer read any old books. Azerbaijan changed in 1924 from Arabic-based to Latin-based, then to Cyrillic in 1940, then back to Latin in 1991.
