One, there is no real downside to taking them other than their cost.
Two, there are definite and dramatic benefits to taking specific vitamin supplements if you're deficient. E.g. if you don't get enough vitamin C in your diet a supplement will protect you from getting scurvy. A more modern example is iron deficiency, a third of American women are iron deficient. Vitamin D supplementation is recommended in the winter, etc.
So the idea behind the multivitamin is it may help you out with stuff you don't know you need, basically, and also it may not, but you have nothing to lose by taking one.
To date I haven't come across a study which attempts to frame the issue in this light. A study about longevity doesn't really change my point of view: I take them after a night of drinking where a hangover is probably incoming and god knows precisely what I'm deficient in the next day. The medical system's only advice is don't drink and I already blew that one :)
The idea is that the vitamin d improves, but it's not capturing the actual benefits of sun exposure
You can, but wouldn't we expect them to be correlated? E.g., better health and less disease should lead to a longer life (as we assume all non-health related deaths to be random and not correlated to health)
Take two groups of people who live active lifestyles in non polluted areas, who don't smoke and don't have any other health issues (including mental health issues because a lot of them are correlated with a shortened lifetime). Give placebos for one of these groups.
This study would help a bit, but would be impossible : we don't have enough people who live this lifestyle and are available for long testings on multivitamins. They may also change their lifestyle, get into an accident, develop mental health issues, travel...Which would poison the results.
I think no one should take multivitamins expecting to live longer. Take them for the other proven benefits - they counteract deficiencies, that's all. My blood tests already show this, I take a blood test before an Iron Supplementation Cure and after, the benefit is clearly visible on the test.
which might be enough reason to keep buying and eating it, esp. if the cost isn't that high. Even if it is a placebo effect, it has genuinely improved your health.