> There's nothing wrong with running E-Commerce on Wordpress also, as long as your payment solution does not include storing sensitive data such as credit card numbers in the database.

This is just not true. Suppose I get write access to the content your Wordpress site is serving. Now I can replace, say, the Stripe (or any other managed payment solution) JS and HTML with my own, to save the CC info and forward the unmodified request to Stripe. Game over.