That article just strikes completely the wrong tone IMO. It reflects her mindset in that the Fire Service should adapt to suit Jack Monroe's needs, rather than prioritise actually functioning as an effective emergency service.
I hate that anecdote about marrying someone on the opposite shift. I am sure it was a silly throwaway comment, not a serious suggestion.
Maybe they didn't consider her childcare issues, but knowing what we know of Jack, nothing they did would have been enough, and sorry to be blunt but in a job like that in the end it does come down to physical strength, a certain mentality, and the ability to work shifts of a specified length. Sorry, you can't leave a burning building because it's school pick up time. Even someone like me in an office job still has to meet the demands of my role. She doesn't seem to grasp this.
Old sick note would never have lasted as a fire fighter anyway.
Every job has its demands. I couldn't have managed to work as I have without a tonne of family support which I am beyond grateful for. She decided to jack in her job and create drama which she's milked ever since.