The fitter will use the timing constraints during fit, and if the constraints are not met it will try and work harder to meet timing. So once it has met timing, it will generally stop.
Usually, it is not the FMax that people design by, it is the frequency of the interfaces required to get a specific bandwidth.
Eg - if you have a 10G ethernet interface, you will need a 64bit data bus running at at least 157Mhz to service the data rate, or 128bus bus at 79Mhz
This is what usually determines your clock requirements.