Why is it important that a project manager be able to successfully manage the trade-offs of time, cost, and performance?

If the project isn't completed on time, it may be worthless, or have lost the market opportunity.
If cost is too high it will be a financial drain, or may never be profitable; or may have to be scrapped.
If performance isn't up to the mark, what's the use? There could be no takers.
Hence the PM needs to understand the project and its overall context deeply, and exercise judgement. Ex. If the project is behind schedule, whether certain features should be dropped so that it can be released on time? Or are those features worth the delay? Or is the higher cost for certain features worth it? Etc.
Hth