I am very very far from a helicopter parent.
On this one, even I'm afraid I think YABU. It's shit having little ones when you're tired/ill etc but them is the breaks (and I had 3 under 4 so know of what I speak 
DH once opened our front door to a hysterical neighbour whose 3yr old DD (also hysterical) was covered in blood. Ambulance job, facial scar, the works. Mother had turned her back to do something, her DD had literally just fallen over her own feet and somehow bitten her mouth/banged face on the floor. Her Dd was so hysterical she couldn't even explain what had happened.
Yes of course these things happen all the time and your presence itself doesn't prevent them, but if they do happen it's better that you are supervising, or at least awake. I'm pretty sure if my neighbour had been having a "relaxing nap" upstairs, she would have had a visit from social services. Do I win by mentioning social services first? 
I look back at the toddler years with horror, I didn't really enjoy it because it was so full on and wearing. From a distance though, it goes really quickly and this level of supervision doesn't last forever. For the pre school years though, they do need watching out for. Reasonable to leave them to play quietly in safe rooms for short time upon waking, or reasonable to leave them in safe environment for ten mins while you go to the bathroom etc. Leaving them completely unsupervised in the middle of the day, on a different floor, while you sleep off a hangover - not so reasonable.