The funny part is that your expectation is probably "I get the legitimate 1 hour of work instead of them taking a nap" but the reality is "I get 4-5 hours of poor quality work after lunch due to lack of nap".
Make sure to keep the context here. HN on occasion discusses napping at work and nap policies, and the discussion is usually pretty sensible.
This, however, is basically "Should my employer give me a benefit because I'm tired from working for other people?", which is, well, let me settle for "definitely not the same question".
In this case you can make a strong case that the employer in question isn't so much on the hook for providing nap time, but justified in firing you for not being able to keep up your end of the bargain because of your choices.
So wouldn't the answer to this be not to give them paid naps, but to eliminate the reason they need the nap in the first place? Most people take on side work because they don't make enough at their day job. So maybe re-evaluate their compensation and maybe raise it a bit?
This is a never ending cycle of people chasing more and more money. If you're paying them fair market value for the area, then there's little point in giving them a pay rise for asking for a nap because they're tired. Chances are, they're chasing contract gigs because they have their own interests in the work or they just see the dollar signs - I know I do it... but I also know that come 10pm I'm wasted and have to hit the hay to start it all at 6am again the next day.
This, however, is basically "Should my employer give me a benefit because I'm tired from working for other people?", which is, well, let me settle for "definitely not the same question".
In this case you can make a strong case that the employer in question isn't so much on the hook for providing nap time, but justified in firing you for not being able to keep up your end of the bargain because of your choices.