OK - I'll bite. I'll stand up for the electric saws (even though on this site, it probably means people will ask for their 'rep' back).
First the safety thing. You are right. You can still get cut with them - they run the same chain as the smaller gas powered saws. In fact, if you read the labels on your safety chaps (2 more assumptions in a testosterone filled forum) you will see that there is a special warning regarding electric saws. Because they are designed to run at a 'constant torque' they do not stall out as quickly when tangled with the fibers, like the gas saws do.
That said, they are generally lighter and quieter than gas saws. They do not use flammable liquid or require repetitive jerking on the starter cord to get them going. Squeezing the trigger does not cause a torque/moment on the handle. They do not emit clouds of smoke or get as hot. They generally transmit less vibration to the user. More similar in some ways to using a Skilsaw than gas chainsaw.
Safer? One could argue that these factors make them easier to control and less fatiguing to use. Less prone to cause hearing loss, white finger, or burns. Other than that, they are probably as safe or unsafe as a gas saw of a similar size and power output.
I have 3 electric saws - partially due to specialized uses, and partially due to E-CAD. When I am trimming trees or bushes in the neighborhood, I am never more than 100 feet from a 120V outlet and that makes them pretty convenient. No, I have never cut the power cord. And my Makita UC4000 has a chain brake.
No, I can't take them in the woods, and no, I can't cut things that you need a 660 for. But they always start, and they don't need to be 'winterized'. And if you look back at the first Stihls and other saws of that era - they were electric.
Just like gas saws, there are big differences between $30 Big-Box store electric saws, and the Stihl/Husqvarna/Jonsered/Makita/Dolmar/Milwaukee ones.
Philbert