But then they'll just jam another contract in that 4 hours... they won't sleep.

The issue isn't paying the employee to sleep, that's just a symptom of the real issue:

The issue is poor time and resource management or poor setting of client expectations on the part of the employee. They're not setting expectations well enough to manage their time and get the sleep they need to do the job they agreed to do when they were hired.

So realistically, if they're not doing the job we contractually agreed to, this should be disciplinary. If you're not living the life you need to meet the contractual obligation you agreed to, we need to review, renegotiate or cancel the contract. I don't care what you do outside of what I'm paying you to do, but if it's impacting your ability to do what I hired you for, then we need to talk - because I need someone that does what I need them to for us to get paid, if we're not getting paid, how long do you think I'm going to be able to afford to pay you?

I have budgets, product quality, deadlines and client expectations to manage as well. We're a team, if anyone on that team aren't able to function for the good of the team, then that needs to be fixed accordingly.

I agree in the OP's case this is a disciplinary issue. I would argue it's cause for termination but I imagine that's a minority opinion here.

I was referring to hobs's suggestion that a mid-day nap increase employee productivity and work quality. That may very well be the case but I still wouldn't pay employees to nap in the middle of the day.

To be clear, I dont think it is a minority opinion, I have fired half a dozen people for sleeping on the job, it was against policy and it was unprofessional in the workplace I was a part of.

My point is that things we think may be taboo could in fact be beneficial if we are willing to reconsider the assumptions that it is based upon.

Anyway, thank you for letting me play devil's advocate :)

Because I am not asking about when someone should sleep or not.

I am asking if paying someone to do something would produce an unambiguously better product, why argue with the practice unless its harmful/illegal/etc?

If I create software and I find that if I pay my employees to sleep and they create a better product than if they worked for 8 hours without me paying them to sleep?

You can blame the employees, but if you decide to ignore this practice and your competitor takes it up, they will beat you in the market while you complain about paying people to sleep.