I guess I've been spoiled by my case then. Stupid case, not needing screws.
The horror! I can't stand tool-less cases

I don't know, it's just always felt more right to have it mounted internally. It's wierd, I know. Although I don' see how it somehow makes it easier to back things up to. Unless you're talking about using it for an all-around backup drive for multiple PCs.
I never said it made backups easier, I said it makes for a better backup solution. An internal drive is at risk of falling victim to whatever damages the original data. An external drive allows you to unplug it (protect it from surges), isn't powered by the PSU (protecting it from the rare but possible spectacular PSU failure), can be moved away from the case when offline (protecting it from localized physical incidents). These are all aspects you would want in a backup. The more you can mitigate damage to the original data from also damaging the backup data, the better. (this is why mirroring and RAID are not backups)
What's USB 3.0 good for, anyway? I really haven't seen any use for it other than what you have already stated. It just sits there, unused.
USB 3.0 has better bandwidth (as mentioned) and far superior power management. Not only is less power used in general, power doesn't run hot when devices aren't in use, which was a problem with USB 2.0 (plug a mouse into a laptop and it'll constantly drain the power even when you use the touchpad instead of the mouse). eSATA was a hack to increase speed to SATA levels for external devices. USB 3.0 is a proper, durable solution and also backwards compatible with USB 2.0. In real-world situations, SATA III is faster than USB 3.0 (which in real world situations provides bandwidth only slightly faster than SATA II), but most hard drives cannot even saturate SATA II, much less USB 3.0 or SATA III