* s/impeachment/“conviction by the Senate”
Impeachment by itself has been shown to accomplish nothing. There is no other mechanism except conviction by the Senate to address constitutional or legal violations made by the president.
Also no president has ever been impeached by a House which is controlled by a majority of the same party of the President. If Congress had a full Republican majority during Nixon’s years, he would not have been impeached. If Congress had a full Democratic majority during Clinton’s years, he would not have been impeached.
Edit: “Approval voting” is the appropriate escape hatch from 2-party politics. It lets you get rid of primaries entirely and run all the top-n candidates who have the greatest number of valid nomination signatures. Its advantage over range-voting/etc is that it is dead-simple to explain to voters: Put a checkmark next to any candidate that you're "okay" with. The candidate with the most checkmarks wins.
https://rangevoting.org/CompChart.html