A healthy diet not only makes you live longer. It also makes the experience less miserable when you reach an old age. That reason alone should be good enough.
The question is what constitutes a healthy diet, and particularly if the Mediterranean Diet is a particularly healthy diet or not.
Well, for starters, there is pretty solid evidence that the Mediterranean diet lowers the risk of heart disease. I'd consider that healthy.
As far as I know, there is only really significant evidence that people in the Mediterranean have a lower risk of heart disease. This could be the diet, but also the lifestyle in general or even environmental.
There is also the "hill argument". Mediterranean is hilly, promoting short periods of physically intense exercise which has been proven to be vital for health of cardiovascular system (huge UK wearables study)...aka often walking uphill carrying stuff is good for you
It would be funny, but we do have a lot of other data around disease progression that tends to agree.