I think we can look to what happened with the Mueller Report for clues into the motivations here.
Does anyone remember the Mueller Report?
I suspect most that (believe they) do, they remember snippets of William Barr's heavily-edited and arguably very misleading 4-page summary, and administration officials chanting "Four legs good, two legs bad" "No Collusion. Total Exoneration."
Few remember that contained in the Mueller Report are snippets like Trump directing multiple officials in his administration to fire Meuller (which is prima facie attempted obstruction of justice). Few remember that Sarah Sanders admitted the administration's given reason for firing FBI director James Comey was a complete fabrication (again, prima facie attempted obstruction of justice). Few will remember it because Americans don't like to read anything longer than a meme caption.
Similarly, if no witnesses are called in the Trump impeachment trial, then Americans will have to trudge through the pages and pages of documentary evidence, and that's just too much work.
Conversely, if witnesses are called, there is a non-zero chance that one of them will utter a damaging catchphrase ("What did the President know and when did he know it", "it depends upon what the definition of 'is' is", etc.) which will catch fire in the media.
As I've noted elsewhere, the political consequences of the impeachment trial are probably less than attention-hungry media would like us to believe, as neither Trump supporters nor Trump opponents are likely to change their minds on the basis of the trial. But I suspect Turtle McConnell doesn't want to take the chance of a "If the President does it, then it's not illegal" moment on camera.
my2cents 