The only "dead right now" shot is a brain shot. All others take some time. I started going to elk camp in the early 1950s. In 1953 I was allowed to have a rifle and actually hunt elk on my own. The messages were very clear. You shot them in the high shoulder. You did your best to get close. You always checked to verify a hit if the animal did not go down at the shot; and not just at the spot.
A brain shot is a low percentage shot. Chest and shoulder shots are high percentage shots.
Not too long ago, heavy-for-caliber bullets were the rule for elk hunting and Nosler Partion was the king. In our elk camps, the 30-06 was a good elk rifle; the .270 was ok with 150 grain partitions; the .257 was marginal. This has changed somewhat with the advent of bonded core bullets and more recently pretty advanced copper/zinc bullets.
Elk are big and strong and have a strong desire to live and get away if they possibly can. They do not always drop or even visibly react to being shot. I shot a huge old cow a few years back with a perfect chest shot - through both lungs and broke the offside front leg. She bolted at the shot and disappeared behind brush. One might have thought I missed. But there she was dead about 20 yards away. The big 6x6 bull I shot 3 years ago with a low front on chest shot (through the top of the heart) took off with a leap sideways and disappeared into the brush. He ran about 25 yards and piled up, then slid down the side of the hill coming to rest around a tree. When he slid down, we thought he was slipping away by the noise. He gave a death bellow - the only time I heard an elk do that. I cannot remember how many elk somehow found there way down into canyons to die instead of staying up on top as desired. Message is clear. Check your shot every time and do it carefully.
300 yards is far away. Few people know where 300 yards is.
No one knows what the wind is doing at over 300 yards. You can have a hot rifle cartrige that shoots very flat but the wind becomes very significant for drift beyond 300 yards. A flat cartrige helps with minimizing elevation and distance error but is still affected by wind drift.
I hope that my experiences help with the subject. Greybeard/
"Even the Evil Need a Place to Live", attributed to a troll speaking to Gudmundar, Bishop of Holar, Iceland (about 1200 AD).