Yes, I agree with both points. When done right, they're slightly safer and more energy efficient, because there's less current flowing on the full length of the neutral line. I've even seen installs where the inspector was okay with a handle-tie made with a scrap of copper wire, although I'm not convinced that was actually code.
The handle-tie would get you common-trip too, wouldn't it?
No. Over-current trips do not flip the breaker to the off position. Instead, it trips internally and the handle moves ever-so-slightly and becomes “rattle-y” for lack of a more precise term.
If you have a breaker in your hand (now or at a home center), you can slap it briskly against your thigh and it will “trip” allowing you to see how the handle will look when tripped. To a cursory glance, it will appear on (but you will notice the handle can be moved about 1/8" more than normal).
That small movement is not enough to induce a trip or disconnect on the handle-tied breaker. (The requirement is only "Each multiwire branch circuit shall be provided with a means that will simultaneously disconnect all ungrounded conductors at the point where the branch circuit
originates." That's to allow for safe servicing.)
The handle-tie would get you common-trip too, wouldn't it?