That wouldn't work for the same reason you don't hear about framing in general all the time. DNA is just another investigative tool, the idea of it being some magical crime solver is a Hollywood invention; it's not how the actual police and legal system use it. Simply dropping some skin cells (or whatever) at the scene of the crime isn't going to be any more effective in framing someone than sending a note to the police saying "Haha, I did it" and signing your target's name.
That's not to say that framing someone with DNA is impossible, but I don't think DNA is especially prone to this any more than any other piece of evidence you might wish to lead investigators in the wrong direction.