We kind of do. The Okinawan diet is perhaps the best studied in the context of "Blue Zones" and they consume no olive oil. In fact, their traditional fat consumption is something like 6% of calories. Similarly, the Sardinians did not consume as much olive oil traditionally, as they do nowadays (56% up): https://ucdintegrativemedicine.com/2017/05/sardinia-centenarian-secrets/#gs.bcr052

I am not saying that substituting olive oil for vegetable oils or animal-derived fat is bad idea, but just adding olive oil and thinking it will miraculously protect you is not really supported by much evidence I have seen. For example:

"...any oil—including olive oil—is not a whole food and thus has little place in a whole food, plant-based diet. Like any other oil, olive oil is a processed, concentrated fat extract and thus has lost most of the nutritional value of its original form (the olive itself). If you want some nutritional value, you will find it by eating the whole olive—not by consuming it in its almost unrecognizable extracted oil form.
To evaluate whether or not olive oil is indeed ‘heart-healthy’, we first need to understand a few facts about vascular biology. The vessels in our entire cardiovascular system are lined with highly functional endothelial cells. These cells provide a barrier between the blood and the rest of the body tissues and are involved in blood clotting, the formation of new blood vessels, and recruitment of immune defense cells.
 Endothelial cells also produce nitric oxide (NO), which makes blood vessels dilate to increase blood flow and prevent platelets from sticking to the vessel walls. Impaired endothelial function is a hallmark of vascular disease, considered an early event in the development of atherosclerosis, and seen in patients with high blood pressure, high cholesterol, coronary artery disease and type 2 diabetes. A noninvasive method to test endothelial function is Flow Mediated Dilation (FMD), which uses an ultrasound to measure flow-mediated changes in the diameter of the brachial artery. Healthy endothelial cells will respond to a stimulus by releasing NO and causing the brachial artery to dilate, while unhealthy cells will not. In other words, the level of dilation (or lack of), measured via ultrasound, is a good indication of the overall health of the vessels in the cardiovascular system.

...
Not surprising, significant FMD impairment can be seen after someone smokes or eats a lot of fat, sugar and/or salt in a meal. FMD impairment is also detected when someone suffers from mental stress or a chronic disease like high cholesterol or diabetes.

So what is the effect of olive oil on FMD?
All oils, both animal and plant derived, tend to worsen endothelial function. Within hours of ingesting fat, arteries stiffen and the ability to dilate is impaired.

A 1999 study measuring FMD after the ingestion of high-fat meals reported a “3-hour decline in FMD after subjects ingested a traditional meal of a hamburger and fries or cheesecake. Olive oil was found to have the same impairment to endothelial function as the rest of these high-fat meals.”

And a 2007 study showed a similar detrimental effect on endothelial function after the intake of olive, soybean and palm oils. Is Extra Virgin Olive Oil a Healthier Choice?
In a cohort study designed to measure the effects of a Mediterranean diet as the primary prevention of cardiovascular disease, extra virgin olive oil (EVOO) was shown to be better than regular olive oil, but neither significantly reduced heart attack rates.

Other studies report similar findings, showing that EVOO damages endothelial function—just like its ‘regular’ olive oil counterpart.

In the PREDIMED study, 7447 people at high risk for cardiovascular disease were randomly placed into 3 groups. One group was told to eat a Mediterranean diet using only EVOO (up to 1 liter per week!). The second group ate a Mediterranean diet and added half-pound of nuts per week. The third group was told to reduce fat intake (but it didn’t).

After five years, the conclusions were stunning; there were nearly no differences between groups. No differences in weight, waist circumference, systolic and diastolic blood pressure, fasting glucose, or lipid profile.

And no difference in the number of heart attacks or deaths from cardiovascular disease; those in the EVOO group suffered just as many heart attacks and cardiovascular disease as those in the control group (there was a significant reduction in the number of strokes, but that reduction was greater in the group that ate nuts). ..." https://ucdintegrativemedicine.com/2016/05/why-you-should-opt-out-of-olive-oil/#gs.bcopqu