So anyone can do philosophy without even trying? That makes the term "philosophy" pretty much meaningless.
There are professional philosophers, and there's the rest of us who do philosophy as part of our lives and normal thinking process. It may be conscious or unconscious but we all do philosophy. I think this makes it more meaningful than just a job.
As for what the word "philosophy" means... that could be a non-productive discussion. You will agree that semantics are a treacherous field. I am happy to go by the ethymology of "the love of wisdom", but your way of defining it (asking "the big questions") works too.
People doing science don't need to study philosophy, read philosophy or care about philosophy. I suppose if they do philosophy by accident, it won't hurt anything.
As I said already, science cannot function well without a certain ethic involving respect for facts anf for other scientists' results. This ethic is not just pragmatic ("what works for science"), it is also grounded in philosophy of knowledge, aka epistemology.
Of course, some scientists are unethical. Sometimes it works for their career, sometimes it doesn't, but this is not to say there's no ethic in science.
Science also assumes a certain universality of knowledge, which is a philosophical principle in that it underpins science but cannot be proven empirically. (Mathematics are supposed to be universal, and replication of experimental results is a key test of truth in science: if you do an experiment in the US and i do the exact same experiment in Europe, the results should be the same, otherwise there's something fishy somewhere)
More personnaly, sometimes it does hurt to be unconscious of your own philosophical beliefs, because these frame how one sees the world, they filter your observations and influence your interpretation. It's important to realize that, I think, in order to guard somewhat against one's own biases. In other words it usefully humbling to soul search a bit. Hubris is never a wise thing to have, not even for a scientist.