$0.02 FWIW
There might be a (albeit) slight advantage to turning off inexpensive white LED strings (aka Christmas strings) during the day. The white LEDs use fluorescent phosphor to make white light, and the real cheap ones have a seriously short output expectancy due to use of cheap fluorescent material. I have a 2006 string of Christmas LEDs tucked up under kitchen cabinets and under a coffee table to make a nice soft glow. Especially useful when walking a dark house at night. I can detect a reduction in light output compared to when they were new, so have resorted to Socket Rockets in hopes of doubling their useful life as opposed to leaving them on constantly. I would guess the LEDs made for true residential lighting (under cabinet strips, rope lighting, etc) are of higher quality, since a Christmas light is assumed to only work a month or so per year.
Only food for thought.