It really depends on the employee's role and duties as to whether it's workable or not. I work in L&D and manage a team of trainers and we can offer flexibility around this, with some caveats. But not all jobs can.
We do have parents who work in a similar way to this, they have to organise their days so that they do meetings/training sessions before school/nursery pickup and their admin work during the last hour or two of the day, so that kids are not disturbing any client facing work or important meetings. Everyone works remotely except for occasional away days and travel to client sites to do training.
Sometimes there are requirements for later training sessions/travel to client sites. Evening sessions and travel to site have to be shared fairly within the team so it doesn't always fall on those without kids/older kids, as many of those staff have other responsibilities too. We agree with individual employees what reasonable notice is for parents with younger children for those engagements so they can pre-arrange childcare for those times, and this goes on the flexible working agreement. Most parents tend to be happy with 1-2 weeks notice.
If a parent comes to us and says "help I can't get childcare for that day" of course other team members will step in. The issues, where we've had them, have been where a staff member didn't communicate and then dropped it on me last minute that they hadn't got childcare and either I've had to rearrange my entire diary at short notice to cover the customer's need or ask another team member to.
We have only ever had to withdraw this type of flexible working once, because someone just wasn't managing things properly and we ended up with kids shouting in the background on a customer training session. I think the staff member had just crossed their fingers and hoped the kiddos would stay quiet, but they didn't. Because we give a lot of flexibility, dishonesty doesn't go down well.