You can round an image with CSS, but (correction per conversation with @Starx) You can't round an image with CSS and it wouldn't give you a benefit anyway because you are only masking sections of the image. The bytes that are hidden are still there and they still have to be transferred to the user's browser, so you don't have a bandwidth benefit even if it is a transparent PNG.
Furthermore, you will be hurting your self (ever so little) because in your style sheet, the code you'll have to write to perform the effect will actually add overhead to your style sheet. Thus you will actually be adding more data to be transferred to the browser and increasing your bandwidth usage.
Option 2 in your question is more appropriate when dealing with images. As far as why the rounded corners was added to CSS, it has nothing to do with images and programmers [sucking with PS...]. Some of the uses you may see are someone trying to replicate the roundness of the Apple input fields/buttons on their page. Or another example would be
div's that need to act as panels or modals.
Really, there's no defined usage, it's just a matter of convenience on whatever you're working with.
The CSS needed to round an object across all browsers that support rounding:
border-radius has to be last because that is the proper property by specification. For more details, please go here.