Why seven days

A seven-day inspection interval is not tradition, it is arithmetic built on the queen cell's own timeline. A swarm cell goes from egg to capped in eight or nine days, and the old queen typically leaves on the day that first cell is capped or within a day or two after.

If you inspect on day zero and see no started cells, the colony cannot produce a capped cell before roughly day eight, so an inspection on day seven, one day inside that window, always catches the colony before it can depart.

Stretch the cycle to ten or fourteen days because the weather was inconvenient, and you lose that guarantee, since a cell begun the day after your last visit is now well past capped and possibly already gone.