Interesting ideas, I've always thought the umbilical setup is the way to go. Have the gas and oil on a belt or backpack, and an ultra light but big engine. Electric powered ones could be very good too if they knew how to make it as good as possible, but if they haven't perfected their gas saws after all of these years, they won't come close on the electrics. I was wanting to build an electric saw at one point in time, more work than I had time for. They get the most torque when they are under load at low rpm VS gas getting the most power at higher rpm. In terms of efficiency gas at full throttle not cutting burns about as much fuel as when cutting, but the energy is just wasted when not cutting. An electric motor uses what it needs, so at full throttle without cutting it barely uses any power, so it barely wastes any. But in the cut it will draw and put out a lot of power. Although not ideal to have no clutch, an electric would be harder to stall the chain in a cut than with a gas saw. A gas saw is also limited to a certain max continuous power output with no higher burst output while a well built electric motor the size of a coke can could do 3-5HP continuous, and short term peak 10-20HP for 5-30 seconds. The big issue is run time VS power output. Even though electric is more fuel efficient, the energy density of gas far outweighs the energy density of any available battery by like 50 times. That's why diesel electric is so popular because you get the energy density of diesel coupled with the efficiency of electric motors, and ideally a small battery too to store energy from an idling engine.
I've always wanted to try a diesel saw. An unusual design I thought of a month ago was a diesel engine backpack with a hydraulic powered saw. Still it would suck to mess around with fuel/oil/hydraulic lines, but you could always have a quick connect no leak line system. Another design I'd like to see in big saws is a farther forward hanging front handle for better balance and control, and definitely a longer rear handle for more leverage, and diesel power. They could also fit a lot more gas in those handles, probably twice as much if done right, but then where would the extra oil go so you don't run out?