What's the huge cost? Most land reptiles and mammals spend most of their time idle anyhow, including humans. In many cases sleep is arguably preferable as the animal is less likely to get itself eaten. If you're not foraging or reproducing, your best bet is to hide and stay still. Because animals, especially land animals, tend to be specialized for particular parts of the day or for other scenarios which preclude 24/7 activity, there's not much that can be done in that idle time. Except improve neurological function, apparently.

Animals that need to be constantly in motion have other adaptations.

For modern humans the cost can be immense according to our cultural calculus. I'm not sure it's an evolutionary cost. Only time will tell whether those burning the midnight oil have better reproductive success.