You can not volunteer to be layed off.
They will be careful to lay off at the Correct Proportions of male/female/races and allowing volunteers prevents that.
Why would it reflect badly on the company if voluntary layoffs are not the perfect gender/race/whatever ratio? That's not on the company. No way could that be used against Medtronic. I think a voluntary round would have been a perfect idea.
Another problem with a voluntary program is that the company may lose employees that it wants to keep, ending up in a weaker (or less talented) team sharing the work of members who selected the program. The company could always say no to the persons who volunteered. But they may become disgruntled.
MDT offers voluntary program before. You will have to apply and they decide. More recently General Motors did it and 5k employees took it and it’s enough people to not need a layoff. So it can be done and should be offered after VERP.
I could see it being a problem if it ended up showing that certain demographics were more likely to leave voluntarily depending on what those were. Let say for example, women chose to leave at a higher rate than men, it might imply (or some may infer) Medtronic is not a good place for women.