Is it all right to actually pull the whole dead stalk out of the plant, once it has flowered?
Certified GKH Gardening Expert
I would recommend cutting the stalk as close to the base as possible. Pulling the entire stalk may cause damage to the roots. Here is some more information: https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/cutting-back-agapanthus.htm