However it's supposed to work in theory, the House delivered a sentence to the Senate, not a case. Not one exculpatory witness was permitted nor were clearly pertinent documents allowed to be entered into evidence.
With what they were delivered, the Senate is actually a group of lawyers looking at either the defense presenting the case for dismissal, retrial, or a plea bargain that falls short of the theoretical single sentence the Senate can deliver which is removal from office.
Looking at what is going on in the Senate and comparing it to any other trial not tossed out as a mistrial as soon a mistrial is requested is a bit silly. The House threw out first presumption of innocence, then the right to confront your accuser, and finished up with denying the defense the right to call witnesses or exculpatory documents.
Given the specific circumstances of this circus, what you're arguing is that the Senate should be held to the very same standards that would have prevented the House from ever delivering the articles of impeachment in the first place if the House had stuck to those standards.
JMHo
No, what I'm saying is the Constitution gives the Senate the sole right to try the impeachment. Period.
Putting arbitrary restrictions on how they conduct that trial, like barring new evidence, may be fair, reasonable or defensible but it isn't Constitutional.