..flown competently just about any twin will be able to execute a shallow climb on one engine. Typical single engine service ceilings are around 8K.. some lower, some higher. For that to work you have to be well above Vmc, and flying at Vyse, and the plane has be free of unnecessary drag, this means flaps and gear need to be up, or come up ASAP. You also need to do everything right in that first few seconds of failure
I have been flying twins almost exclusively for the last 2 years.. the duchess and Aztec will fly along merrily all day long at at least 6K. Once you retrim flying on one engine is really a non event. My DPE was a big fan of the Aztec, he had a fully loaded one lose an engine over Brazilian forest and they flew on for 3 more hours on one engine. All lived.
People get burned, and you have the whole "second engine only flies you to the scene of the accident" because, and this is just my opinion:
(A) people don't practice true single engine ops enough (or ever). They do their multi training and check ride, buy their 310 or Baron.. and then 25 years later when it happens in real life they screw up. I was talking with an aerostar pilot and instructor, even that will fly just fine on one engine.. if you are competent
(B) sometimes it's better to just pull the power back in both engines and do a controlled crash, as in this case. If you JUST took off and have the gear down there's no sense in forcing the thing to fly and risking a Vmc roll, pull the power back, and put her down
As a statistical anomaly, you don't hear about all the successful single engine airport landings. Our own club had one a few months ago no issues. For a while there was an Aerostar at Ramona with a blown apart cylinder, they made it down safe. Talk to lifelong twin pilots and most will have some story about a shut down. When I'm flying over water, at night, or over mountains I'd much rather have a second engine with redundant systems and at least have a chance at surviving.. vs a near guaranteed death sentence