The baby stage is a relatively short one. Parents might need to take time off from time to time all the rest of their working lives - even when the kids are grown up! Our head of HR recently took a month off to look after her daughter who had just had a baby.
That's why it's wrong to think of this as just a parenting issue. Other people need flexible working hours too, for example if they have aged parents or neurotic pets to look after. And if we sort it for parents we sort it for them too.
Would it really be that difficult to say to employers (who often also have family responsibilities) that if someone makes a reasonable request for time off, to let them have it? A log could be kept, and if someone appeared to be taking more than, say, five days in a year, they could be asked to account for it.
As for the maternity/paternity thing, what would have made my life easier was to have been allowed to take a year off, instead of 6 months. However, everyone is different, and there really is no one-size-fits-all solution.
Couldn't some law be designed that reflects that fact?