It wouldn't change how the public thinks about them. People wouldn't understand how voting machines work, even if they were open source. Do you expect normal people to look at and understand code? Also people who have lost hope in democracy and want to believe that the election was a hoax will continue to do so anyway.
It's probably more comfortable for the manufacturers of those machines to keep them closed source. Why would they show the world how they work? That would disclose potential flaws which is bad for their reputation. And it would make it easier for competition to emerge.