It seems that the framers of the Constitution wanted a 2/3 majority
to prevent a partisan decision.
In other words lawmakers on both sides of the political spectrum
had to agree that the President had done something wrong.
The 2/3 majority (mostly) prevents one party from dismissing the President, as can be done in England---a parliamentary form of government---,
just because they don't want him in office.
In the American Constitution the 2/3 majority falls to the Senate.
But the framers could have required that the 2/3 majority fall to the House.
In Trump's case, if the 2/3 majority was instead of the Senate, a requirement of the House,
impeachment would have failed.
The House would have needed 54 or 55 more votes to reach the 2/3 requirement.
The conclusion is impeachment is a bi-partisan undertaking,
and the 2/3 requirement pretty much insures one party who dislikes the President
cannot forced their opinion on America without the help of the other party.
So in the present case 2/3 of the Senate is required,
but regardless, the House, even though Dems are the majority,
could have never gotten a 2/3 majority