The legitimacy of the Supreme Court relies on keeping it as depoliticized as possible. A Keep Nine Amendment would help keep an already over-politicized court from losing its independence altogether.
While I don't know that our present political atmosphere would allow us to mount a serious effort to amend the Constitution in this manner, I wholeheartedly agree that all possible efforts should be made to keep the Supreme Court at its present effort. The last thing we need is for each political party to take turns adding additional members each time they control the wheels of government in a back-and-forth attempt to control the composition of the Supreme Court. Where would it stop? Could see a Supreme Court of 20, 30, or more justices? This would be a disaster. Hopefully enough Democrats can see the sense in keeping the Supreme Court at its present level to join Republicans in stopping any court-packing scheme and, eventually, see what can be done to amend the Constitution to keep such a tactic from ever being considered.