It all depends on the T... my B. albopilosum (curlyhair) will have a cricket in her fangs before it even touches the ground but others like my N. chromatus (Brazilian red and white) are more skittish and I have to squish the heads of the crickets she takes. You've just got to be careful because feeder insects left in the cage can cause huge amounts of stress to the spider and even inflict serious wounds on it when it is fragile during molting.
The early bird gets the worm... but the early worm gets eaten by a bird.