Tiredness is a signal that the body/brain needs rest so the glymphatic system can go to work. You can lose the signal but still need rest. If your brain doesn't flush metabolic waste periodically you develop brain fog, bad memory, and increased risk of Alzheimer's, and you'll eventually die, as sleep deprivation studies have found.

Caffeine doesn't actually do any of the things sleep does to your brain. If you drink coffee during a late night, you won't feel as tired, but your brain performs worse, your reflexes are slower, you're less likely to remember things, etc. It's like painting over a rusted car instead of properly maintaining it, basically.

Isn't the answer yes if people still die from overwork despite being caffeined up?

If I’m on morphine is my leg even still broken?

You have the ability to mentally push through a lot of stuff, but there are a host of signals your body will use to warn you such as: cognitive performance (although this is hard for yourself to actually admit its happening), behavioral indicators like yawning, head bobbing, frequent posture changes, and slowed speech are just a few indicators. Irritability is another big red flag.

I've only had two instances where I ignored all the signs and continue to push on until my body literally shut down on me. Finals week in college as an architecture student trying to finish a final studio project, and study for four finals. 5 days, 3 hours of sleep. That was one of them.

Michael Jackson is the ultimate case study for this.