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This leads me to my question: is it fundamentally always the best to let the fitter dictate where pins go?
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It depends, but usually the answer is no.
If you have many tight timing constraints involving signals to or from pins, the Fitter is sometimes able to shuffle them around to improve timing. However, if you place the pins yourself and the Fitter does not issue any errors or warnings, and you successfully close timing, it means the placements you picked are probably just as good as what the Fitter would have done.
Cheers, Adrian