Whether its electric or gas, a base thick enough to evenly spread the heat, will always be better. With plenty of thermal mass, a mark:space switching power control, with say a 30 sec or 1 min cycle, shouldn't give much temperature variation. Whereas it would, with just a lightweight bare element.
Only burning I've had, seems to be mostly due to settled flour or particles, forming an insulating layer, rather than sugars in the wort. But not sure if your kettle burning, was with an all grain, or extract brew.
Had an incinerated bottom incident in, my BZgen4 (with false bottom and heat exchanger dish), with an overheat shutdown for a while during boil. Shutdown happens at a base temp of around 120°C.
Afterwards I found there was a 6mm deep burnt black crust, over nearly the entire base. Apart from a few narrow channels, that must have been kept clear by the (slow) mash recirculation.
23l Brew was a Weisenbock, (6.5kg grain, 50% wheat), After vigerous drill stirring at dough in, it needed stirring multiple times due to slow recirculation /stuck mash . With all the stirring, lots of flour and small particles must have been carried through the malt pipe base, and false bottom, to settle out on the base.
Beer tasted extremely smokey. Ended up giving the entire batch away.
Revised method now, involves minimal gentle stirring. only at dough in, just to break up any dough balls.
It's not ideal that the BZ false bottom and HED dish, are covering it's heater base during the boil (though they catch some hop crud). Running recirculation during boil, helps avoid hotspots, but I occasionally still end up with a very thin 'tanned' layer in places.
If I had more room, I'd try separate mash; sparge water; and boil vessels.