Interesting debate, my first dish washer must have lasted around 25 years, free standing type. But last house the counters must have been deeper, as with this house the dish washer does stick out about 3" which is handy as lower than the microwave above it so a ledge to put coffee on while we shut the microwave door.
But more important to if integrated or not, is how easy for maintenance, and how well it washes dishes, and for how much. I am not sure what all the programs are for, one would need a degree in dish washing to work out the best program, we always use the same one, so not sure why we have so many.
However we do have one extra feature from the earliest model which we do use, the delay timer, after dinner I can set the dish washer to come on around 1 am when we have off peak supply, over the evening we will open the dish washer many times to put in the extra cup or plate, but no remembering to turn on before going to bed, it will auto start.
Same with washing machine and tumble drier, we have three high power electric using items auto switch on when the power is cheap.
The problem in going for integrated anything is often they lag behind with technology.