Don't think so - originally there was no need for a J because I made a Y sound as in
Iulia; then as the sound changed, people needed a newletter to accommodate the new noises they were making.
You're right about the middle ages - spelling wasn't standardised so anything could be flung into the mix. That led people to stick in Y spellings in order to make medieval stories etc seem authentic. The result is often inaccurate kitsch, but if it doesn't bother them why should we complain? Just avoid Ye Olde Elisabythanne Coffye Shoppe...