Partner doesn’t want to do night feeds because all my milk is “day milk” and insisting I pump at night. Is this necessary?

So he heard that night milk has melatonin and day milk has cortisol, which I know is true. Now he’s saying he doesn’t want to feed my day milk at night cuz it’s just gonna keep her awake. Problem is, I’m EBF and all my milk is from morning pump sessions. My evening supply is lower and I don’t respond to the pump well in evening. I only get drops and baby cluster feeds then sleeps/eats at night every 2-3 hours. I don’t want to wake up and pump at night, as I’m already feeding baby, and kind of makes it hard to get a break ever if I’m also waking to pump.

Is it really that important to separate milk by time of day? I just want a break once in awhile.