Not very many people DO try to copy the great painters, but when they do, they are often quite successful. A competent technician certainly CAN copy them. Students copy them with varying degrees of success, and forgers copy them (by definition) with great success. The thing is, there are few enough "well known" painters that there's room for distinctive styles.
Photography is so easy, there are so many photographers, and it is SO easy to copy someone else, that of course we have endless overlapping bodies of work that all blur together.
I do not think that it makes sense to think of "style" in the same way. My thinking is that the serious work in photography has to be portfolios. Any individual picture might be a copy of this or that, and look kind of like the other thing, and so on. But a complete portfolio can still have a distinctive look. Loads of people have done cinematic photos. Only Cindy Sherman would put together a set of 59 of the things, all with the same girl in them, all with the same general flavor (which flavor itself only becomes clear when you see multiples, really).