In the first place, Congress doesn't impeach only Presidents. When it comes to anyone who is impeached, there are three separate decisions. Although they are separate, yet the second and third don't occur if the first is decided in the negative.
1. Removal? Yes or No.
2. Disqualify from future office? Believe it or not, a removed official can hold office again except if the Senate decides to also disqualify them.
3. Guilty? Believe it or not, removal does not constitute a finding of legal guilt. If the government chooses to prosecute a removed official this is done separately in a court.
Second, the Constitution was based on a reaction to the British parliamentary system. The parliamentary system does not separate the executive and the legislative branches of government. The reason that a President is impeached in the Senate is one that may surprise you.
Until 1913, the Senate existed for the PRIMARY purpose of giving the governments of each of the States a voice in the National government. The framers intended that Senators make decisions which reflected the combined will of the State governments. That is why Treaties were to be confirmed by the Senate. That is why the Senate has the power of Advice and Consent in the selection of the President's cabinet and that is also why the Framers chose to give the Senate power over the decision of whether ""The President, Vice President, and all civil officers of the United States" are to be removed from office.
Today, the State governments are impotent in the National government. But the original plan of the Framers was that the combined will of a majority of the State governments expressed through the Senate would have clout in the running of the National government.
This was part of what is called "the checks and balances" of the federal system.
Sadly, over a century ago, there were problems within several state governments pertaining to the selection of the Senators. Seats in the Senate sat vacant because the States which were supposed to select Senators for each of those seats were having internal squabbles within the State governments.
In frustration, the Congress proposed removing the power of the State legislatures to select the Senators. Since most of the States were not having this problem and since those States which were not having the problem were getting upset with the States which were allowing these seats to sit vacant (and since people tend to choose short-term solutions over a consideration of long-term consequences) most of the states ratified this proposed amendment.
The reason that today we have situations in which a large number of States band together to sue the national government in court is because the State governments are no longer able to resolve these problems through the Senate and because they've been left out of the loop in the legislative decision process.
Your suggestion would weaken the "checks and balances" even further and it would add a burden to SCOTUS which is ALREADY over-burdened and has a difficult time keeping up with all the requests for its attention, some of which are mandatory.