Wafer level testing is very difficult because the bond pads have to be contacted by long needle(without impacting the bondability). Thus the test mostly is checking all parameter which make sense that gives you good final test yield of the packaged device. At package-level you have leads from the package with good contact areas which can be more easily connected without any damage.
With special test boards to can then run then very detailed test to verify functional and parametric performance at different temperature levels.