Can I get rid of my sump pump?

My job moved me cross country and we bought a house (3 yrs old) that sits on a hill. It has a walk-out basement and the hill slopes away from there, yet the house was built with basement drainage going to a centralized pit and sump pump.

We are going to finish the basement, so I want to make sure it never floods, but the power can easily go out in bad weather. Instead of buying a secondary pump, battery backup, etc, can I just tap into the current drainage bed and use gravity to drain down the hill? Could I dig down near the low corner of the house, find the drain pipe that feeds into the sump well and connect a drainpipe that goes away from the house and down the hill instead?

I know the drain pipes currently in place are sloped to drain toward the centrally located sump well, but as long as they are all below basement floor level, then they could “back up” to my new connection point and drain down the hill without the water level rising high enough to flood the basement, right?

The only negative I can think of is that the water in the sump well (and the other drain pipes leading to it) may get stagnant since they won’t ever empty (my downhill drain would essentially drain from the top of the current system), am I missing anything?

I guess I could break the concrete slab and dig a trench from the current low point (sump well) out that side of the house and drain down the hill, but I would like to avoid all that concrete work if possible.