Ubercart

Yeah if you already have a content type called product you'll need to remove it first and then re-install Ubercart.

Interestingly, if it was called anything other than 'product' you could create a product class out of it. Basically the uc_product module would take control of that node type and start using it as a product. You can only do this for user-created node types because module-created node types would lose the functionality that the module first gave to them. And that's not what you want, generally.

That's a roundabout way of saying that the Product node type doesn't do that because the module is trying to add the node type to Drupal from scratch.