If 'every President will be able to appoint at least two Justices during a four year term' then the ideological leanings of the Court are likely to change more frequently.
This could result in the Court 'flip-flopping', where it constantly changes its decisions on important policies.
Supreme Court appointments have become more and more partisan in recent years. As parties controlling the presidency tend to change often, the ideology of appointees to the Court will change more frequently as well as exacerbating polarisation because this process occurs more frequently.
While ideologies in the Court may change, rulings are bound to previous binding precedents, potentially limiting the impact this may have.