This question came up while teaching ~16 year olds binary numbers. Why do place values increase to the left and not the other way round?
This is probably better suited to the History of Science and Mathematics SE, but I'll take a semi-informed stab at it.
Since we read from left to right, placing the most significant digits in that same order give us the best opportunity to quickly comprehend the magnitude of the number. For instance, the speed of light is 299,792,458 meters per second. I think your brain is much more equipped to jump to "Oh, around 300 million" by seeing the most significant digits and the number of commas than if the number were given as 854,297,992.
We obviously had a lot of history before the Hindu-Arabic numbers came into existence. But even things like Roman numerals would give you the ability to just think about the degree of precision you wanted by ignoring the "digits" like I and V and X and L that you felt like ignoring.
Our numbering system comes from copying the Hindu-Arabic numbering system. They write from right to left, so in their system, they start from the least significant digit. However, taking over the ordering as-is was easier, otherwise operations would need to have been adapted. So we write numerals in the same order even if we generally write text in the opposite direction.
Note, that some operations are more "natural" in one order, others in the opposite. Comparison and division are naturally done from the most significant digit, addition and multiplication from the least significant digit.
Also note, that this is connected to endianness which is relevant for computer systems.
It makes perfect sense if you consider the full range of real numbers instead of just integers. In any base (decimal, binary, hex, whatever) the radix point (decimal point in base 10) is in the middle with exponential powers increasing positively to the left and negatively to the right.
For any base ß :
ßⁿ + ßⁿ⁻¹ + ... + ß¹ + ß⁰ . ß⁻¹ + ß⁻² + ... + ß⁻ⁿ
This works in binary as well as any other number base. In fact it used to be common to operate on scaled binary like this in lieu of floating point.