Some miniscule percentage of computers will fail prematurely. Your question isn't whether it's worth testing at all but if you test, is stress testing better. The starting point is that your machine is the one in 10,000 that will fail prematurely and your goal is to cause that failure. What is the best way to make that happen? (When it doesn't fail, it has passed the test.)
There are a bunch of different parts that could be what fails and the trigger could be simply energizing the system for a short time, it could be heat in general when the system warms up, it could be a specific component getting hot, it could be mechanical (vibration or thermal expansion and contraction), etc. There is no way to know which part or which trigger will be the cause of the premature failure.
If you just turn the system on and let it idle, that might be enough to trigger a problem sensitive to energizing the system or general temperature. If you run Memtest86+, that will test the RAM. If you run a comprehensive stress test, that is likely to push many more triggers than not running it. The more things you test and the longer you test, the greater the likelihood of finding (causing) the failure.
I would venture to say that no statistics exist (at least available to the public), on the actual benefit of testing in any specific way. The premature failures are too rare to generate meaningful numbers to tweeze apart the benefits of one kind of testing over another, or the benefit of testing for one time period or another.
If you happened to be the unlucky soul who got that ill-fated computer and you spent a lot of time setting it up and accumulating critical files and then it died, you would probably be pretty miffed. So is it worth doing some type of out-of-the-box test before you start using it? What could it hurt? If you decide to test it first, the most useful test would be the most comprehensive stress test you can find because that is the purpose of the exercise.
Absent any solid data on relative benefits, you have to make a "management decision" on how much testing will satisfy your comfort level. Something to ponder: suppose you test the heck out of it with no problems and then spend time setting it up and accumulating critical files and then it dies anyway. Would you be more miffed than if you hadn't spent the time to test it first? That's another decision factor.