Is there a historical reason for this or is it completely arbitrary?
It's arbitrary. But, I have a question for you. If you ask me why I choose Ł for /w/ when W is free, then why does Polish choose W for /v/ when V is free?
At the time the Latin alphabet was adapted for Polish, v
wasn't "free"; it simply a variant form of u
(which, of course, Polish was already using to represent /u/). These letters didn't become distinct until about 1500 CE, by which time the Poles had been writing their language for hundreds of years.
oooooooooh, i see.