As far as I know linguists came to conclusion that most of the modern alphabets initially derived from the Phoenician Alphabet, which belongs to the Semitic branch of the Afroasiatic family of languages. Phoenician basically invented the idea of the Alphabet, that eventually spread to other cultures, and through trade routes.
Most of the modern European languages use some variations of the Latin and Greece alphabets, because the Ancient Greeks and the Latins had close cultural interconnections and trading routes with Phoenician colonies, and these two civilizations were the most developed European cultures in ancient times.
As I understand it, the Phoenician Alphabet was a simplified method of communication in a sense of a trading information transmissions in contrast to more complicated systems of hieroglyphic writing. But naturally the Phoenician Alphabet follows the basic ideas of hieroglyphic writing too. Such as the letter Alep (𐤀) depicts an ox, and it basically means "livestock", and the letter Bet (𐤁) depicts a house, and it refers to "domestic". Having these letters as the first letters of the alphabet makes sense in the proto-semitic culture, because the livestock basically refers to the amount of wealth in a subsistence farming economy, and the house refers to an economic agent (a household).
But such hieroglyphs make no sense in the Indo-European family of languages. At first glance even if the ancient Latins had kept their alphabet set as it is, they at least had to take different images and choose different phonetics for the letters. The Latin word for "Alpha-Bet" probably would sound more native as "Bos-Dom" in this case.
Nowadays, there are a lot of attempts and related research in developing new artificial languages. I'm wondering whether there has been any research in developing of new alphabets in the sense of the glyphs depictions and their phonetics that would better fit the Indo-European family of languages, and the historical cultural aspects (such that the letters would at least reflect the most important PIE roots).