Remember Donna? She became the most important human in all of history. And it worked because she wasn't the point of the whole series - she wasn't trying to get into the Doctor's pants and actually had some character. She was just another random everywoman, who didn't have a lot of faith in herself. She followed the Doctor around and slowly grew into someone who was kinda awesome in her own right, who worked as a foil for the Doctor and also as our eyes and ears in their journey around the universe. Since Donna, the companions have become the Doctor's reason for existing. They are the reason he goes anywhere, does anything, says whatever he says. His entire life is dedicated to working out why the companions are the way they are, who they are, and what they are.
It's perhaps not surprising the show has come to this. The cult of the individual has never been so prevalent as it currently is. All our TV shows are aimed at convincing us that we could be famous for being nothing at all, that our story is important, if only someone would listen ... the cult of the individual companion since Moffat's reign is what you would expect from that.
The companions are no longer important because they have a certain strength that comes from their abilities, from what they achieve. No, latterly they are seemingly born with this amazingness already built into them. Donna, Rose, and Martha (love them or hate them) all went from ordinary to extraordinary, capable of being worthy companions in the actual equal companion sense of the Doctor, because of how they grew through their experiences with him. Amy and Clara both appear to have some sort of inherent importance right from the get-go, which frankly leaves them utterly boring and incapable of development in any meaningful way. Rory fit the Donna/Rose/Martha mold, because he was a seemingly ordinary person who wasn't that great, and ended up doing some very great things, which perhaps shocked even him because he didn't think he had it in him.
If you can take any message away from what the companions are supposed to signify, it might be, perhaps idealistically, that each of us has the potentiality to grow and realise our own importance and worth. Each of us can be great in our own way. Unfortunately with the last two companions that message has got turned on its head. Their characterisation suggests that some people are born great. You don't need to work for this, you get it handed to you if you are lucky. And that "specialness", endowed by providence, places you at the centre of the universe.