I was at The Getty Villa yesterday in Los Angeles, and noticed they have an overwhelming amount of Vases, Bowls, and perfume holders from Ancient Greek and Roman times. I'm pretty sure I remember this being the same at other museums I've been to... Am I wrong and is this just a fluke of the particular collection of that Museum? Were bowl and vase shaped objects just particularly good at surviving through the years? What the heck was put in all these fancy delicate vases?
Sorry but this is more of an Engineer's answer than a Historian's answer. It has to do with the materiel of the vases.
Ceramics are actually super sturdy, they are basically artificial stone. If they are preserved in such a way that prevents them from being crushed to dust or exposed to repeated freeze/thaw cycles they can basically last forever. Things like metal tend to rust and degrade over the years, and cloth will degrade even faster. So I suspect that a big part of the reason why you find so many bowls and vases and such at museums is a consequence of the materiel used to make them.
If there is a historical answer and the Greeks were really just into pottery I am happy to be corrected and informed. I just thought I would contribute a possible materiel engineering answer to the question.
They used their pottery for almost everything you can think of, food storage, for water, wine and oil, to serve food, to drink from, to play drinking games, to store cosmetics, and specific pottery was also used for burials (to store the bones or ashes, as well as special oils or perfumes). The fancy delicate vases you saw were likely to have been for cosmetics or oils, and one of the major reasons why so many of them have survived is because they were often buried with their owners.