What's the benefit? Assuming enemy age up at 3|15 - by the time the enemy reaches Classical age and you're even on villager count again - they'll have had what? 240 seconds of extra resource gathering if my math is correct?
Hmm I just checked it, it didn't have any effect on training time. It's a habit from going first to hunt. You are going to lure a hunt (boar type) and want to kill it faster. Since TCs fire more arrows when empowered.