I'm the one who puts my little boy to bed ... and we'll everything else for that matter. I like doing it all though - either that or I've just got used to having no help!
I do bedtime most of the time but if I need a break my husband will do it. Communication is key x
It should definitely be shared (sensibly - depending on what else he's expected to do). I do the night because my husband works, but he wakes up if I need him (poop explosion LOL) and he often takes him in the morning before work. I'm struggling a bit (baby is 3w) so thank God he WFH and can come down and help sometimes. Earlier he took the baby and I made dinner, as I needed a break.
I think it should be shared but as time has gone on my partner has fallen asleep holding our baby and ended up in the bed with us so we agreed that I would just do it moving forward. It’s caused lots of arguments though if I’m honest.