Real travertine? Yep. It is necessary. Travertine is marble. It is made up of calcium with a few other minerals mixed in. Calcium is water soluble....it can be dissolved using water and some cleaning agents. It will take a lot of time....but it will happen.

The way to stop this = sealant. Travertine, in the lower quality stuff, is crumbly and is pitted. Dirt embeds itself into the pits (which is why they use filler on it) and then the water gets in a causes more damage.

And it stains. And etches.

All of these issues are greatly reduced by sealing travertine and marble. You are welcome to leave it raw but you probably won't like how dirty it gets and how hard it is to clean it. You will rinse and rinse and rinse and rinse and yet the floor still looks dirty and the mop bucket continues to come up muddy.

Grain cut travertine (which is a higher density and higher quality) will be easier to live with....but it still needs sealing. It is marble after all.