First, nothing should be "hanging". Your octo should be neatly routed under your right arm and clipped off to your chest in a way that it easily releases. If someone comes up to you and signals that they're out of air, the last thing you need to be doing is feeling around for an octo floating somewhere off in space. It's likely that a panicked diver who is out of air would simply rip the reg out of your mouth, so you'd either have to scramble for your octo yourself or fight the panicked diver over who gets the regulator and lives.
As for why a regular second stage for the octo, the important reason is that in a real emergency, you would donate your primary reg to your buddy and switch to the octo/inflator combo. Because the hose for your primary is relatively short, you and your buddy would be nose to nose as you make your ascent. As the octo combo hose is even shorter, you would lose the ability to turn your head right without the mouthpiece coming out of your mouth and, if you had to dump air out of your BC as you ascend, you would be manipulating the buttons on the combo at the same time as you're breathing from it. It's just a high stress situation as opposed to donating an octo on a hose to your buddy, who can stay an arms length away while you manipulate your inflator assembly during ascent. Many recreational divers make the decision that out of air situations are uncommon enough that it's worth the chance in exchange for one less hose, but I think many people (aka me) bought one because they never thought through how they would be actually used in an emergency. Note that if you ever eventually go into technical diving, you will be required to use a standard reg as a backup.
Also, inflating a surface marker buoy at depth when you have an inflator/octo combo requires switching to the combo and using your primary regulator for inflation, since it's the only one with a long enough hose, and then switching back. Depending on where you dive, inflating an SMB could be done every dive or could be a strictly emergency procedure. In any case, it's easier with an standard reg octo.
Buy a batch of stainless steel EMT shears off of eBay for less than a dollar each. They're designed to be single use and sharp enough to cut a person out of tough clothing, and are cheap enough throw them away as they get rusty or get dull with use. You can buy a sheath for them, but Hashime's suggestion of just attaching them using a clip, or clipping them to an attachment in your BC pocket would work too.
