the main reason you see deep belly bars on the bike saws is,
the gear on those saws are quite big the 18 tooth is 4.42 inches in diameter so you need the bar to be bigger than that at the mount to the gear or you will break , pound , jump ever chain you got on it. So now the bar has to get bigger so you can keep the drivers in the groove because of all the chainspeed the chain will grow . On that saw with the 18 tooth it has a bar that is 7.50 inch deep in the middle and when you nail the throttle it still picks the chain up alot , plus it takes less power to go in a oval than it takes to go in 2 straight lines with sharp corners
