yeah that is a big deficiency. I recently took a course on Coursera about early cities and all of it was about the Phoenicians! It was from Sapienza University and it focused on archeological findings in one location in Sicily. Apparently the place was a Phoenician pitstop on the way to Spain. This is the course if you're interested
We don't know a lot about Phoenician heritage and culture because there hasn't been much budget or public interest. As for culture itself, the Phoenicians as a distinct cultural identity and people have been pretty much extinct. They all emigrated!!