Those are my favorite style of balusters, so I would hardly call it polishing a turd. With that said, balusters are easy enough to replace. There are a ton of YouTube videos. You can also get just plain square wood ones that are a little less fussy pretty inexpensively.

If someone can put these in (someone did), then someone else can take them out and put in wooden ones that aren't so "country" looking.

Wood is one of the world's most malleable materials. You could have square, round, whatever. The problem is finding them, of course--but plain 1x1s or dowels aren't that hard to find.

Also, look at those buttons on the newel post--those cover screws or bolts, and that's how you could take them off.
A carpenter might be helpful, if you don't feel that confident.

Here's someone's Pinterest board that shows other designs in wood.

https://www.pinterest.com/pin/450852612689018467/?lp=true

and another pic
https://www.pinterest.com/pin/499125571192479077/

If you happen to be doing a black/white thing with your decor, I'd try painting black before replacing them.

Those are pretty classic looking spindles - seen in older homes and newer.

I removed the carpet and painted my spindles:

My pics -work in progress: · More Info

I do like the idea of choosing a paint color that's a bit of a statement--it'll distract. And the black that's shown, especially because it's on the stairs as well, actually minimizes the shape of the spindles because the stairs fall behind them.

I bet the knob on the newel post screws off; maybe there's a hole you can cover before you paint. That might minimize the effect of the design.

I don't know if there's a tube you could split and then snap around those carved spindles. Or if you could cut artist's mat board into strips to glue onto the sides spindles, thereby converting them to squares by covering up the grooved parts. Probably would look cheap.

OK, some other paint notes: The ones where the spindles are the same color as the wall, but the railings are in contrast, really downplay the spindle shape--that's one idea. So maybe paint the spindles the same color as the wall (and in matte, perhaps; certainly eggshell), and paint the railing to match the gloss white of the woodwork.

The newel would be best in the railing color--and you don't love that newel. If taking the knob off the top doesn't tame it enough, it might be easier to replace than the rest of it. And cheaper--an unfinished solid square post, primed for painting, is $40 at Lowe's.

https://www.lowes.com/pl/Stair-newel-posts-Interior-railings-stair-parts-Stairs-railings-Building-supplies/4294512335

Personally, I might go with a newel post with a little more detail so it doesn't seem like such contrast to the spindles. Those are under $100.

(plain wooden balusters are only $4.13 each--the labor would be the biggest thing. I'd be SO tempted to try to unscrew that newel post and see how the balusters go in, to see if I could actually replace them)

IMO removing the carpet on the stairs would be a huge improvement too.