Or you could remove the carpet, insert risers via the backside and paint the whole thing, then add your runner on the stair side. The challenge will be where the stairs go over the badly added maids closet from the 50s....oh wait those are my ugly carpeted riser less stairs....ummm anyhow the first part of my answer is how I'm going to deal with the issue :).

You could still do a runner effect. The country club where I grew up had open riser floating stairs and there was wood exposed on each side with a piece of runner attached around each step.

I would recommend keeping the handrail and the tread stained If thats what the treads are--its hard to tell if they are even wood. rather than painting them white: more durable and the bit of wood against the white will provide some highlight.

I have a link for you. It's in our Gallery among the room threads, and staircases have a huge thread all their own. There are some open staircases in there, so keep scrolling for them. Don't think any are carpeted, but I agree with you that carpet is better with kids and dogs.

Here is a link that might be useful: Staircase Eye Candy Blowout!

These might work. It seems they are only in the UK, but see what you think.

Here is a link that might be useful: Clear stair treads

Wow... thanks for all the great ideas!
I had wondered whether finishing them off on the back so they aren't open should be considered. Just afraid it will make a small room seem even smaller so not sure. There was a photo in oceanna's link towards the bottom that I liked where the staircase is finished off behind the steps and they have the driftwood like paneling/shelves and some beachy stuff on them.
Loved the staircase candy link -what great ideas there! And just fun to look at.
I think the other idea that could really work is still doing a runner, but rather than wrapping it around the whole step like I originally thought was the only option...is looking at some of the 'stair tread mats' that were in deedees link.
Love the sisal mats! seems we could keep the openness and not have such a "heavy look" of carpeted steps.
Filing these ideas away! DH has a ways to go on the remodel but want to be ready!

I don't have an opinion one way or another, but here are some pictures I found where you can see different options/colors etc.

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Vinyl flooring on threads - not as slippery

inset with trim

Sisal to place on open stair threads
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A link to a google search with open stairs

Here is a pic of open stairway with runner:

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This has really helped! I am finding more ideas now that I know to google "carpet stair treads" rather than runner or just "open stairs".

Nice to know there are other options to a fully wrapped step. Seemed to much for the beach.
Thanks for getting some new ideas for us!

I think I like these styles with a painted/stained stair.

Glad you found my link helpful, and what a lot of great pix here -- didn't want you to miss them! Hope you will post some "after" pictures of yours.