It is really frustrating to me that so few rely on their common sense with this topic. As a single page can only have one title, and it is the clearest indicato

It is really frustrating to me that so few rely on their common sense with this topic. As a single page can only have one title, and it is the clearest indicator of what the page is about (it is the TITLE), of course it is important. It is also the main determinant of whether someone will click on your search result after, of course, rank. But we're also talking about "onpage SEO" here, which is like 1/1000th of what determines if you will have a successful website in search engines (and even less for a successful website, period). You should know the basics, then worry far more about the quantity and quality of links to your pages... and lots of other stuff.