An interesting observation from Prof. Freedman (Hofstra); I think that, if such a rule were adopted (and I don't advocate it), the result would often likely be Presidents and the Senate reaching a compromise on a truly centrist Justice—but I might be mistaken, and in any even the thought experiment is worth considering:
It doesn't take a lot of imagination to foresee a period in the near future in which Presidents only get to fill SCOTUS seats when their party controls the Senate. Both Senator McConnell and Senator Schumer have hinted at this possibility.
How would that play out? At minimum, this hardball paradigm would create a lot of lumpiness in the filling of seats. The number of sitting Justices would gradually dwindle during periods of divided control and then a President would get to fill a burst of them.
More troubling is the possibility that the number of Justices might dwindle to five. Then—because by law a quorum of the Court is six, 28 U.S.C. Sec. 1, S.Ct.R. 4—SCOTUS could not act at all. Essentially, the last word would be in the lower courts. See, e.g., Arunga v. Obama, 137 S.Ct. 2194 (2017); Jaffe v. Roberts, 137 S.Ct. 2192 (2017); 28 U.S.C Sec. 2109, and the discussion here.
