I assumed it was due to the height of the ships that typically passed. Probably costs more to build the bridge higher so you don't have to raise it as often, so they fight about lowering costs and minimize the number of times they raise the bridge.

Power consumption to open a drawbridge should not be extraordinary. The bridge leaves/moveable sections are counterbalanced.

Traffic mainly, but also maintenance. Mechanisms needed to be inspected/serviced every N openings. Although the big fight was basically that 'Team Road' wanted the bridge to open twice a day at fixed times and if a boat missed its slot it just had to wait, while 'Team River' wanted the bridge to open within 10 minutes of any boat showing up.