I had to WFH for the past few weeks with my toddler because her nursery closed for a while, and we have no other option apart from me or her dad taking unpaid time off which we couldn't afford to do.
Her dad did two days WFH with her but his job only allowed it begrudgingly, and there is 0 downtime at his job at all. Whereas my boss offered for me to WFH as long as I needed, I do have downtime but I'm expected to take calls when they come in.
It was NOT a treat or a nice relaxed few weeks WFH. Couldn't leave the house in case a call came in, toddler bored, always seemed to want me as soon as the phone rang, I'd miss calls because of doing a nappy change or putting her down for a nap. I explained all to my boss and he said as long as I return any missed calls and get all my work done then he was ok with it. It meant I had to put off a lot of work until she was in bed for the evening. Didn't even get a proper break when she was napping, she only has one nap a day and it ranges from an hour to an hour and a half so i used the spare time to catch up on work.
The I'd find work was quiet and as soon as I'd sit with her to read a book or play, anything that wasn't putting the TV on for her her, that's when there'd be a sudden surge of calls or tasks and it was so unfair to her.
So it may be doable but you have to have the right job for it and you need to sacrifice a lot. So actually no, it isn't doable. I'm very lucky that my boss allowed it, but unfortunately my partner will never be able to WFH at the drop of a hat if she's not at nursery for whatever reason. He earns more money than me so I guess it makes more sense for me to risk my work than it does for him. It is not fair but it's the way it is.