Well these numbers originated in Arabic, and since Arabic is written right-to-left, writing numbers in Arabic actually follows a more logical order: start with the lowest-order digit, and move on to the higher-order ones.
Apparently when the concept was brought into Europe, they failed to account for the different writing directions.
• "Arabic numerals" aren't Arabic. They're Indian. They come from the Brahmi script, which is written left to right.
• The prevailing numeral system being replaced, Roman numerals, also placed the most significant digit on the left, so it's unlikely that this was something that was simply forgotten.
• Western languages (usually) mention the most significant digit first when reading the number out, which makes it convenient for it to be written that way as well.
The entire time the positional notation didn't change with alphabet
Actually, the modern positional system was created, in its entirety, in India. This includes the use of zero.
al-Khwarizmi gets credit largely for introducing the Indian system to the Arabic and Western world. He is the reason that the Arabs and Europeans use Indian numerals, though they've since mutated in look over time.