To be frank, this isn't a debate. Looking at retail as a whole it is very clear that certain items require fancy packaging and others do not. However, packaging ALWAYS matters.
At Target, I expect my razors to come in a secure package. At Nordstrom, I expect the sales associate to package my items with care. Two different stores, two different experiences, packaging matters in both cases.
On another note, my husband is in marketing and he spends HOURS on packaging. I doubt his company would invest so much time in packaging if it didn't matter.
The much bigger problem is that people are not calculating the true value of their items and then are running a business at a loss. Packaging should never cut into your profit but it is a very important part of your branding.