For things like high pitch BGA chips mounted on PCBs (like everything in a modern PC), the thermal stress of turning on and off is much more damaging than having it running all the time. They are just like light bulbs. On/off stress is much higher than constant-on stress.The short version is that a product generally lasts a given average number of hours... how quickly you use them up, is entirely up to you. Having your machine on *all the time* is going to use those hours up --substantially increasing the likelihood of a failure-- probably two or three times as fast as someone who has to common sense to turn things off when they're done with them.
MTBF only makes sense for things like fans, which are cheap to replace, and last a very long time anyways. I keep all my desktop computers running all the time. With high quality brushless DC fans, they wear out in about 5-7 years. They only cost $4 each.