That is a good point. I think that it would be far more interesting for a character backstory if the character originated from Zaun.
Example:
The character grew up in Zaun with a passion for science. It was his dream since he was a little kid. However, when he actually started working in a laboratory, he realized the immorality of the experiments. He decides he wants to be a scientist for Piltover. He gets in contact with the Piltovian Science Bureau (not sure if that exists, just made it up), and for weeks he writes inquiries and sends photos of the labs projects. Unfortunately, however, he is caught red-handed when a colleague finds these messages. The character must flee, so he grabs the latest project the lab has been working on: a hextech drill, designed for mining toxic substances and using them to make chemical weapons. He then runs off, and stops at the border of Piltover. He's taken into custody for possession of the hextech drill. However, a scientist from the bureau (could be Heimer, Jayce, or a new character), recognizes the drill, and takes the character under his wing/gets him a position.
A bit of example lore, but I do think the whole Zaun to Piltover backstory is a cool one.