Briskly could, in the heat of the moment, be applied too much and tip the aircraft inverted.
I have found the term very useful in understanding that being unenergetic about forcing the nose down promptly will delay the recovery, which could mean non compliance with the requirement that the single engined plane be recovered in not more than one additional turn. Yes, it is possible to get the nose too far down in some types, at some C of G positions. Too far down, will delay recovery a little, but more importantly, will result in a serious dive during recovery. If, at any point while flying a certified plane, you push the nose down so briskly as to end up unintentionally inverted, you need more basic flying practice.
The recovery of the Cessna Grand Caravan, for example, is vastly different at both C of G extremes, yet Cessna had to publish
one procedure which works in all cases, hence "briskly". They condition the term with "... Far enough to break the stall.", and advise the pilot that "Full down elevator will be required at aft center of gravity loadings to assure optimum recoveries.". This, I can assure you is true! I had to briskly apply and then hold full nose down elevator, yet the nose would not go below the horizon for the first half a turn. But, using the Cessna procedure, the plane recovered compliantly, which was what I was testing to confirm.
So after spin testing a dozen or so types, the thing I have learned the most, is to read what the manufacturer published in the flight manual, and do that.