Well, if you're a single mother, it's undeniably tough, because you presumably (and it's a big 'presumably') you get no respite.
I haven't walked in your shoes for one day, let alone a week, so I wouldn't dream of judging you for nugding your child to self settle.
That said, I don't find being at home with a toddler easier. I tend to go out for the day and walk her for her 1-2 hour nap in a sling (yes, at 20 months) between activities. Then when we are home
I also find I can be more testy if I've had a really bad night and it's hard to keep up the steady chatter and gusto and enthusiasm to which she's become accustomed.
I'm lucky (and unlucky) that I've always survived well on little sleep and prior to having a baby probably got by on 5-7 hours and in my job I've always had very early starts and late night schmoozing. My husband is used to doing round-the-clock newsroom shifts.
I know SAHMs who have CCed, working mothers who co-sleep. I think confirmation bias is strong in this emotive area and you'll see examples that back up your view and gloss over those which don't. I just don't think you can generalise.