Its surprising the FAA has not mandated a reg for that to be required for all GA multis. In reality a twin should be much safer than a single
Well, here's how it works. Take your GA multi - Let's say it's a Seminole, which has 180hp/side, a MGW of 3800 pounds, and a single-engine service ceiling (the altitude at which the plane can climb 50fpm with one engine inop) of 3800 feet DA.
First of all, a transport-category plane can continue takeoff at V1 - They have to, or they'll plow into "stuff" off the end of the runway which could include expensive and/or living things. A Seminole, OTOH, has an 880-foot ground roll so plenty of room to stop if you lose an engine on the ground, and no real V1. In fact, the Seminole can get up to 50 AGL, lose one, and still put it back down on a 3000-foot runway.
But, let's say we want to be able to continue takeoff if we lose an engine right at rotation. How do we do that? More power, of course! Climb comes from excess horsepower. By my calculations, getting 500 fpm out of a Seminole at sea level on a standard day would require about 230 hp/side instead of 180 at the same gross weight. Well, that means we need to upgrade the engines. An IO-540 weighs 180 pounds more than an O-360, so now we have 360 extra pounds of engines. That also means we'll need a beefier airframe to handle those engines, as well as about 60 more gallons of fuel to maintain the same endurance. So, now we're talking a 4600-pound airplane instead of a 3800-pound one, so we're closer to 280hp necessary to get that 500fpm climb on one engine. And that's at sea level on a standard day.
Now, since it seems that you'd like to have safety be a sure thing, we need to consider several more things. First is field elevation. 95th percentile field elevation in the US is 4,660 feet MSL. Take a place like that on a hot day in the summer, or Leadville on a cold day, you'd probably like to see 500 fpm at 8000 DA, and that means that you're going to need... 377 hp/side! Uh oh, our 300hp IO-540 won't even do the trick any more - Now we need to add turbos, more structure, and more fuel to do the job. And now, people are going to expect at least a couple more seats and some more carrying capacity for all that power and fuel burn, so up it just a bit more and you're over 6,000 pounds.
The point of all this is - If there were a regulation stating that even light twins had to be able to climb out the way transport category planes can, there simply wouldn't be any light twins any more. It's just not feasible to have an airplane that can do that at such a low weight.
Yes, twins should be safer than singles - But most of that is, like in all things aviation, the pilot's responsibility. If you want your twin to be safer than a single, then don't load it up to gross, especially on a hot day or at a higher-altitude field, if you want to be able to continue a climb-out. However, in many cases (field elevations <1500MSL, not-hot days, not loaded all the way up to gross weight), even the lowly Seminole can in fact either get back onto the runway (from <50 AGL) or continue to climb out above obstacles long enough to get back to a runway. You just have to know what the variables are and stack the deck in your favor as well as stay proficient in handling an engine-out situation.