I doubt that presidents, Senators, interest groups, and others would suddenly stop caring as much if justices served only 6 or 8 or 12 years. A lot of the divisiveness stems from party polarization in Congress, which is not likely to go away anytime soon. Under term limits, I would foresee an increasing number of equally divisive Court battles. Indeed, they might become even more divisive because leaders would know exactly when vacancies would arise, making them even more a dominant consideration in campaigns.
As I said in the earlier post, what bothers me the most about the current system is the arbitrary aspect: if Justices are fairly partisan (which is fine with me), then I'm not really sure that there's any decent justification for the random distribution of deaths and retirements across presidencies. Of course, basically this is all just good August speculation; given that in practical terms reform is basically off the table, since it would require a Constitutional amendment, and that's not going to happen.