You understand it could have been dismissed, the Senate could have even chosen not to hear it.
The House offered their prosecution, they called every witness they chose to present and turned their completed case over to the Senate.
It is no ones problem except the House managers that they did not complete their job before handing it over to the Senate. They had the opportunity to have every "witness" heard they felt needed to be heard.
The Senate's job is not to to open discovery again and complete an (as the House manager's actions proved) investigation.
@Benben, this is for your edification as well.