It does not make sense.

Noting that you to tired during your drive, means you're at the edges of your physical ability. \~that is not ok\~. It means you need to stop and sleep. Or sleep near work so you can have the appropriate alertness to drive home.

Your request sets up a situation, or encourages a situation that puts you, and everyone else on the road, in danger. If from start to finish 12 hours puts you in a physical condition that's poor enough you're looking at lane keeping features to keep you safe, you need to be closer to work.

Everyone can define their income as hourly. You need to calculate what you're making based on the hours you work regardless if you're making salary or hourly. Because commute time, is time you can't dedicate to other things in your life, it is "work" time.

Driving is also not free. This commute costs you a minimum of $30 each time you make that drive. Assuming you make 100k/yr, you make roughly $48/hr. Lets say you work 4-10's (you said you don't commute every day, I'll even give that you work 4 days a week) Your 40 hour week, actually costs you 52 hours a week. That takes your pay rate down to $37 dollars an hour. Throw in gas costs (assuming 35mpg) You're actually making 35.4/hr.

If you lived half an hour from work, under the same conditions, you'd be making 43.7 dollars an hour. And you'd have an extra full workday of time to do things for you.

The math gets worse if you drive 5 days a week.