I've interpreted your question as, "How important is it to become cultured as individual people rather than to rely on our broader cultures to provide us with values and knowledge?" I hope that's similar to what you meant.
My perspective is that individual cultivation is very important for many, although not all, people. Each person's learning and development eventually comes full circle and makes up the collective. When you engage with some cultural artefact and walk away with a new thought or perspective, it may start to inform your actions, and/or you could discuss it with those in your circle. They might think it over and share it with people they know. Even if they don't, it might plant the seeds for them to do their own reflection and seek out new avenues of learning. I think that on a general level, this is how cultural change can materialize.
So, developing one's own mind and perspective is important because doing so can and will impact broader society eventually. It also has a lot of personal benefits and IMO is good practice for its own sake.
edits: clarity