Sati-Sampajañña and a quiet mind Is it the case that a quiet mind can best execute Sati-Sampajañña because there are no interfering thoughts disturbing it?

If the answer is yes, should the main concern in day-to-day life be to tranquilize the mind, to think and keep wisdom in mind, or even both?

Regards
The quiet mind is ideal but not a forced quiet mind. It is only the quiet of jhana that is ideal. If jhana is too difficult,  and unlikely for us, then best not to waste time and practice momentary samadhi instead by becoming aware of the busy, unclear mind when it arises. If there is an urge to fight it or if there is disliking it, be aware there is disliking. Mindfulness impartial to the defilement, the defilement is automatically abandoned, disappears for that moment. Train this way for those who aren't clearing the mind correctly or easily.