First let me rectify something in what you said, "..accurate estimation is the key to a successful project manager", and not to a successful project. Even if both the cost and the schedule estimates are immaculate, the project may still fail (there are many examples...).
Having said the above, accurate estimation is still critical to the project (though not as critical as many believe), as it is based on this estimation that the project is selected/prioritized, and the stakeholders approve the project. If a project is finished way too late and above the planned budget, then its ROI will probably no longer justify it, and this is how projects get canned.
I agree with you that thousands of years ago time was not an issue, but we live in different days right now. The pyramids were built by slaves, so the cost of labor was almost entirely free back then, I suspect that any of the projects that we have at the moment are being executed by slaves. Additionally, thousands of years ago, competition was not an issue, nowadays, if you don't finish the project on time, then you will be eaten by competition (who's most likely working hard on a very similar project). These days time is of the essence, and in my opinion, having accurate time estimates is much more important than having accurate cost estimates, regardless of the project, and regardless of the company.