It would be interesting if the Supreme Court had term limits. I agree that the appointment of a justice would not have the impact it has now. Justices are not supposed to have political views, but those with political views can strategically retire or step down to ensure that a president with like-minded views can appoint another justice with those views. The biggest problem, though, is that if justices has term limits they would be more political not less.
I would agree that term limits for Supreme Court Justices is a bad idea. With the way things are now it allows for consistency of the interpretation of laws. I feel it also takes the politics out of the Court System to at least some extent.
The framers of the Constitution provided that Federal Judges and Justices should serve "during good behavior." The purpose was to ensure the independence of the Judiciary from undue interference by the Executive and Legislative branches. One assumes that if Judges were term limited, they might be more responsive to public opinion than to the Constitution itself which they are sworn to uphold. Presidents would indeed have more influence over the court, but this apparently was the very situation the framers hoped to avoid. One need only consider Franklin Roosevelt's "Court Packing" plan to see how the independence of the judiciary might be compromised. Obviously there are abuses: a number of federal judges drew their salaries while serving prison sentences because they refused to resign and the impeachment process moves slowly. Even so, the potential problems of lifetime appointments far outweighs the potential for abuse.
In my opinion, the main impact this would have is that presidents would not be able to maintain their influence so far into the future as they can now. A second impact would be that more presidents would be likely to get chances to nominate a justice or justices.
As things are now, a president can nominate a justice when he or she is quite young. For example, Pres. Bush nominated John Roberts when Roberts was only 50. Now, Roberts is likely to be on the Court for at least 30 years and Bush's influence will still be felt 25 years from now. Pres. Obama has done the same thing with Elena Kagan -- she was 50 when nominated.
If justices had term limits, each president would be more likely to get a chance at nominating a justice. A justice could not stay on the Court and only retire when a president they liked was in office, for example. This would be fairer, I would think, because it would take the element of random chance out of it -- why does one president deserve to appoint justices more than another one?