Spot on Jack for "older types"! Multiengine aircraft designed from about 1959 (sorry, can't remember the exact date) had to be able to maintain a certain amount of climb performance with a critical engine failed at V1. This later became known as a net takeoff flight path or gradient.
BTW if you're flying/have flown the DC3 & company, I'm jealous! Those aircraft have all been grandfathered with regards modern performance demands. As you've stated, the best you're going to get with an engine out is wings level (actually up to 5 degrees of bank into the good engine[s]) straight ahead.
Unfortunately as airports grew in number and locations became more precarious (mountain 5 miles past the departure end), and aircraft failed to avoid contact with same, the newly formed ICAO developed procedures for aircraft certification and eventually what to do and where to go (Special Procedures as Jepp calls them).
When a modern day aircraft cannot meet the net take off flight path requirements as determined by a whole slew of factors, designers of runway/airport analysis data (there are quite a few with varying philosophies) see if a turn or combination of turns can guide the aircraft away from obstacles horizontally until the takeoff segments have been completed. That's it in a nutshell. It gets pretty complex in the detail.
So if as in Las Vegas the special procedure involves a turn, a radial intercept, a DME
restriction then another turn, followed by another radial intercept, then that is what has been determined to be "safe" to allow an airliner (DH8 or 747) to depart a runway at the maximum allowable weight.
It's a safety discussion and it's a corporate/commercial discussion. All wrapped into one big complicated bundle.
That's why the pay us the big bucks.