I would leave it... water pools in our niche & drives me nuts & I do have a solid piece there...

The niche looks very well done. If you do decide to redo the niche with a tile bottom, all the tile inside it will need to come out because the gap at the bottom is currently sized for the stone's thickness and not for a tile's thickness. Removing that tile will make a mess of the substrate and you may have to patch it. All in all, I think you're better off replacing the stone with a whiter stone or piece of quartz. You could probably get an offcut of plain white Caesarstone for minimal cost.

Yes, the Travertine will provide a better waterproof surface overall. However, the tile setter can certainly finish the bottom of the niche with the subway. He will need the same bullnose tile as on the sides. Is it as waterproof as the stone, no. is it still OK, yes, over time with water on it, the grout could crack and lift. Best shower grout is epoxy over cement-based.

Best waterproof grout:

https://www.google.com/search?client=firefox-b-1&q=best+waterproof+grout&sa=X&ved=2ahUKEwij7-ex1pjgAhVSYK0KHUd7ArQQ1QIoAHoECAUQAQ&biw=1481&bih=753

^ I agree! I think it looks great and I would leave it alone.

You are the customer. You should get it the way you want. Having said that, I think the way it is installed is the better way. Easier to keep clean and will shed water rather than grow mildew. I'd keep it.

Leave it.

Ask him to change it to white white quartz if you can't live with it.

Not that it makes a difference, but that's not travertine; it looks like marble. Currently the vertical pattern in the niche matches the pattern outside in the photo; removing the ledge and changing to bullnose will require the niche to be redone and the lines won't match up because tiles are thinner.

The single piece bottom will be a bit easier to clean. However, it should have nothing to do with waterproofing, as that happens behind the tile. I tiled my niche with all subway tile. There are grout joints on the bottom ledge, and the soap residue and bottom-of-the-shampoo-bottle residue get in the grout a bit, but nothing to run screaming to mama about.

And you can shed water with tiles by sloping them slightly out, it doesn't have to be 1 piece to do that.

I like the look of a solid bottom piece, but if you don't, then have them change it.

I would leave it. It's a better surface than tile for the base. Can't tell from the picture, just make sure there's adequate pitch to direct water away.

Thanks all for the responses. I was told is was travertine, its the same thing they used on my windowsills which I was fine with because I knew what I was getting beforehand and worked it into my design. I was not told that this would be put in the niche and it's really bugging me. I think its the color not so much the material used. Is there something similarly functional I can use but in white?

Leave it isn't an option because it's going to bug me every time I look at it but I am open to alternatives.

I see quartz was mentioned so I asked if that will work. I'm being told thickness might be an issue.

You could look for a marble that’s the same thickness in a much whiter color. Granite and marble fabricators have tons of little scraps that could easily be used for this purpose and they can slice them into a thinner piece if necessary.

If your tiler doesn't like any of your suggestions (quartz, etc.), then just tell him you want a sill that is the same colour as the tile and that it's up to him to find a solution and up to you to approve it before he installs it.