Wood treads are more slippery than carpet, obviously, but once you have them installed you adapt. I think it's a cool look to do the formal wood landings and then switch to carpet. But don't do carpet just because you think you'll slip and fall. You won't-many houses have wood treads.

It's a sort of big job to change out the treads to wood... and if they finish them you'll have to stay out of the upstairs... probably for a few days during the work. Wood stairs will last forever, that carpet will be gross in a few years. I'd just get them all changed to wood at the same time. Then you can repaint... and it will all be done. Then get a runner for the stairs if you hate walking on the wood.