My husband & I were just discussing this today. I think all LED strips still require a transformer somewhere, and then the wiring that links them. Not fond of that set up. But I don't want halogen or xenon either. Most of the more expensive LED strips will say "5 year warranty", but if just one fails, will they still be making the same style?

In all honesty, we decided to get some that run on batteries, and maybe buy a couple spares. I've even seen battery ones that have a motion detector.

These Commercial Electric Under-Cabinet LED lights should do what you want. They plug in, are available in five lengths, are linkable (directly or via short cables), and have three color temperature settings and two brightnesses. You could buy and link two 36" and one 24" fixture. (Oddly a 36" light is cheaper than a 24".)

Least helpful comment, I know, sorry, but I just saw an ad for under counter light strip that didn’t plug in but was rechargeable. Which means no cord running to an outlet, and I think each light was stand alone, but maybe motion activated? I’m not in the market myself so I wasn’t paying really close attention but if cords and links are a con and depending on how you’ll use them, might be worth looking for