The reason the power of impeachment is in the hands of the house and the responsibility for trying an impeached official in the hands of the senate instead of the judiciary branch is to create a perfect "Check and Balance."
This is because it is believed that the numbers of the Congress would make it difficult for the executive officials, particularly the President, to influence their decision, unlike the Judiciary branch.
Also, because the President appoints the Justices to the Supreme Court bench, it is assumed that some of these Justices might be loyal to the President when it comes to decision time.
Hence, in this case, it is concluded that for the sake of Checks and Balances, the power of impeachment is distributed among Congress.
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