It shouldn't come as any surprise that, like other web host providers, A2 Hosting's unlimited plans aren't actually unlimited. It expect you to use its service like "similarly situated customers." This is like being on a highway. If everyone is going a few miles above the speed limit, you're probably okay, but if you're barreling down the fast lane past everyone else, you're probably going to be asked to slow down.
One thing we learned in reviewing the services listed here (and many more) is that even though the packages are very similar, they are not identical. Some are more security-focused than others, offering anti-spam and anti-malware tools. Others offer a variety of email marketing tools. While most of the hosts we've reviewed have built-in e-commerce, you may want to consider using a more-robust third-party online shopping cart application like Shopify instead.