Extensions that do this terrify me. Imagine a popular Chrome extension, say, Fireshot, with 2 million active installs, selling out. The next update of the app gets shipped with a screen scraper that looks at coinbase.com. Some time after you've last visited your dashboard, it opens a connection on some entirely unrelated site and posts to the 'send' page to send all of your BTC to a third party address.
Or if you have 2FA enabled for sends, just intercept the send POST with an address of your choice, but display the user's originally input address on the confirmation screen. To make it even more confusing, keep a list of transactions:intended accounts so any time the user looks on _any_ bitcoin site it shows the transaction was going to the right account.