Some nurseries let you do half days and then do hourly top ups. Maybe see if you could do that? Also this is pretty standard, to pay childcare that you don't get to use. I pay for 3hrs extra a day x4 a week. It's just one of those things.
Does your nursery not offer school hour days? My little one goes 2 days, one is a full day but only school hours are covered by the funding so i pay extra to top it up. The other day she goes school hours ( my nursery does this 8:30-4) i pick her up at 3:30 so i don’t pay for extra hours. My nursery does charge additional fees on top of the funding each day too though.
Could you not leave him there considering you paying and have a bit of me time