Due to popularity of Protocol Droids, I won’t say Basic was lingua franca of the Galaxy far far away, but Basic seems to dominate the Galaxy far far away. You can find it everywhere and it seems special language because it’s officially used by Imperials and Rebels and Resistance. Even the Galactic Senate used to discuss laws in Basic. You can see Basic as lingua franca in localities like Mos Eisley where different aliens talk in Basic without the help of a protocol droids (those aliens have different native languages). According to Wookieepedia:
Galactic Basic Standard (or Galactic Basic, Galactic Standard, Galaxy Standard or just Basic) was the most prevalent language in the galaxy.
Talking about Chewbacca, he fully understands Basic (because Han has never roared to him). Although his buddy Han fully understands him, he does travel a lot (unlike Ewoks) and his language can give headaches to people (not talking about us; what if Rey couldn’t understand him) provided that he doesn’t travel with a protocol droid.
So far if you have been laughing… Now the main part: the dialect issue. What if Chewbacca can’t produce necessary sounds to speak Basic? This seems unlikely because his roar seems to contain all the necessary sounds. Take an example of the mighty Jabba the Hutt. His not being able to speak Basic should be blamed at his not being able to see the point in learning a new language (maybe, a feeling of cultural superiority which is common among old generation wealthy and powerful people) because I remember his relative (of same species) speaking Basic on Coruscant (Star Wars: The Clone Wars).
Also, I remember playing a video game in which there were at least two Wookiees who were speaking fluent Basic. I don’t know if the video game was canon, but has the Canon or Legends ever addressed the language issues with Wookiees or Chewbacca?
Can Wookiees not speak Basic or is this an issue of Chewbacca? If it’s an issue of Chewbacca, why doesn’t he learn to speak Basic?