If the travertine runs UNDERNEATH the cabinets (it might not...so be prepared) then I would look at leaving it. A floor like this is "timeless". No it is not "hyper-trendy". But that's fine. Hyper-trendy looks "out of date" within 3 years. Timeless means you cannot put your finger on a "date of install". It means it could have been done in the 80's, 90's, turn of the millennium, etc. Some floors can be dated to a specific YEAR...and that's what you want to avoid.

If the floors are continuous, I would try to keep them ('cause who wants to save $20/sf on flooring??? Me. That's who;-P). A crisp white cabinet could be paired with a WALNUT counter top!!! Yep. If you can't get the "wood floor" in the kitchen you can at least get the wood on your counter top.

I suggest walnut to help MATCH the floors (connection number #1) of the home as well as compliment the floors of the kitchen (match #2). We know the travertine works well with the dark espresso floors, so why not go ahead and use the same tones as a counter top?

If you wish to remove the stone, just remember to add in a SIMILARLY expensive product....like slate or soap stone or some other high-value product. Removal of the stone will run $3-$5/sf (stone is a B!TCH to remove) and then subfloor prep is another $2/sf and the cost of replacement materials + labour for install. If you purchase "like for like" product, you final bill for the kitchen floor could be close to $20/sf...without batting an eye.

If you like the travertine then try to save it. If you don't like it, please ensure you replace it with a like-valued product. Your home's resale value will thank you.