How well will LED strips hold up in a kitchen?
Longevity: LED's are generally marketed between 50k-100k hours of burn-time. I installed them throughout my home 18 months ago; none of them have failed yet.

Grime Resistance: For a kitchen, buy waterproof strip lights like these - they'll hold up against steam. You can also fabricate an easy-to-clean cover using clear PVC and brackets

Heat: If the strips are installed correctly, each LED will be cool to the touch. Monitor the installation for excess heat and wire in a resistor if needed.