I don't think it's as big of a deal as people think. Choosing to be able to read your letters seems like a very unlikely reason for rejection in the grand scheme of things. I never saw the point of VMCAS offering it as an option - either make them completely confidential (like in the match) or don't. With that said, do what you're comfortable with.
Most people waive access because of the long-standing perception that being able to read a critical part of your own application makes an applicant look bad, and like stated above, 'why take the chance?' However, If I were in the position of applying 3, 4, 5+ times, or a school told me that my letters weren't great in my previous cycle despite having good faith in my writers, I'd be wanting to see who was writing what at that point. You would be surprised (or maybe not) at how little effort some people take in writing these letters, even if the applicant was the best pre-vet a clinic has ever had. A letter that is only a few sentences can have a negative impact, even if the content wasn't negative.
Can someone verify if this is actually true? Back in the day, you could delete writers up until the point that they submitted the letter, but I'm pretty sure you couldn't delete someone after that.