My question is: why did Peter even feel the need to cast lots in Acts 1? I know that was still before Pentecost but Peter literally just prophesied and interpreted psalms of David! He was clearly in the Spirit when he did that! So why cast lots?
my guess is that while waiting, as they were told to do, what happened with Judas and whether there was supposed to be 11 or 13 apostles was a hot topic, and no one had any clear direction from the Spirit. so they did what was a known, proven thing, to try the discern what God wanted them to do about it.
Pentecost itself didn't answer that topic. as far as the record that we have in the Bible, it wasn't until Paul was called ((much later)) that something that really spoke to those questions came about.
maybe they ought to have been patient?
it's really a different question than whether casting lots is legitimate - - but like you said, absolutely nothing in the Bible says it isn't.