It could theoretically be done, but we have evolutionary evolved using sleep as we know it as a recovery strategy. It has shown to be an advantage.

Birds for example also have sleep, but they evolved in a way that only one half of the brain sleeps at any time because that allows them to keep flying while recovering which turned out to be an advantage.

The resources are needed for the actual activities.

Like you cannot defragment your harddrive while playing a game, or more general you cannot update the firmware of a device while using it.

Digesting food is a big one. You essentially have enough blood (ability to distribute oxygen and calories) to run two of three between your stomach, your brain, and your muscles. One of the reasons working out while on a full stomach causes vomiting is because the stomach is upset about the lack of resources available for it to do its job, so it gives up to protect you from harm.

Alternatively, eating after a long day of work puts you straight to sleep because your muscles need to heal and clean, and your stomach needs to digest dinner. You can't run your whole body at once, and sleep is what we call it when your brain and muscles are turned off to let cleaning, healing, maintaining, ad digesting to happen.