Is it like that trend where some people work 2 or 3 remote jobs?
Most babies spend a lot of time sleeping so you can probably get some work done, but if your child needs you you are going to have to drop what you're doing.
There is no problem if you are honest about this and your employer accepts it, but just as somebody can hold multiple jobs and not come clean about it, it seems like a parent could also dissemble about it.
Also, Zoom has gotten surprisingly good - the "high" setting on background noise for "barking dogs" actually works frighteningly well - people on calls have apologized for their exploding dogs because the UPS guy assaulted the doorbell and we've heard absolutely nothing.