Of course there are no gradients, because the 3D-effect can't create them.
Have you already expanded the effect? If so: bad luck.
If not, try: apply the effect "Rasterize" (set a suitable resolution) and then export to PNG
or try and check the option that renders hidden faces (this one is in the 3D dialog box)
I tried all that but it still shows the lines. I mean, you see 3D images everywhere daily...surely there must be a clean cut way of creating smooth 3D text in illustrator or is it the wrong application to use, which i doubt....
Please show examples of what you're referring to.
Some of these images might be created by just mocking 3D with Illustrators tools and some gradients. Others might have been created in real 3D software like Cinema 4D or 3DSMax