That is simply not true, both with regards to Mathematica and your own package.
Our symbolic tensors are very much coordinate and index free, and can be manipulated without ever introduce coordinates, indices, or what have you. What they lack is calculus support, which is a hard thing to do, even more so without a declarative syntax of the type you use. This is something we would like to circle back to, but there are many things we want to circle back to.
Given that you are defining Dp, which is an inherently coordinate-based (whether you define it as a non-tensorial local expression operator, or as a tensorial connection defined via a particular coordinate system), you clearly are not coordinate free. Where is your abstract connection, if you really want to be coordinate free?
