Answer: They should not be.
Step-by-step explanation:
Reduces Judicial Independence.
When voters have to elect Supreme Court Justices, the Justices will not be completely independent. This is because they will have to be mindful of their judgements in order to please their supporters or else they would risk losing their position in the next election.
Supreme Court Justices should be free of such worries to enable them deliver unbiased judgements that would not pander to the egos of voters.
Politicizes the Supreme Court
The other two branches, the Executive and the Legislature, are highly political. We have had situations where the country has gone into a budgeting deadlock that put the government on shutdown simply because the two major parties were in conflict. Imagine such a situation in the Supreme Court where Justices would have to run for office.
The major parties would most definitely get involved and once they elect justices, they will try to influence their rulings to support either party. This should be avoided so that the Supreme Court can remain unbiased and capable of keeping the politicians in check.