Consider these names, just in the 20th Century:
Chief Justices Harlan Fiske Stone, a law school dean, like Kagan, and then Attorney General before going to the court. Or, Chief Justice William Rehnquist, a Justice Department lawyer, before becoming a Justice. Hugo Black a U.S. Senator. William O. Douglas, a senior federal official with no judicial experience. Louis Brandeis, Felix Frankfurter, Lewis Powell and Earl Warren, all without prior judicial experience and all who became celebrated justices of the U.S. Supreme Court.
In fact, every president from FDR to Nixon appointed at least one justice without prior experience on the bench.
Given the extreme partisanship that surrounds all judicial nominees, Kagan will have to run the confirmation gauntlet and answer questions about everything she has ever said, written or done. Fair enough. It is a life-time appointment, but not being a judge - as American history shows - certainly shouldn't be a prime factor in the confirmation test. Until fairly recently it hasn't been much of a consideration at all.
By the way, for students of the Supreme Court, the SCOTUSblog may be the best source around for really good information on the nominee, what she has said and done and what others are saying about her.