They get in excess of 25 days annual leave as it is and can surely use this if they want to spend their child's birthday out of the office.
It's one thing to make the life of a parent easier (such as having meetings after 9.30am). It's another to give extra days' leave where childless employees carry the load.
But I like your thinking, Architien. It would be fab to brainstorm ideas to make companies more family friendly, and then muddle through the practicalities and fairness to the wider workforce.
For me, personally, what I would love is for all stress to be taken away from childcare. That particularly means how you can continue to do your job when your child is ill. Unfortunately, in my job, my children aren't allowed to be ill and the only times so far that they have been off school DH was able to juggle his work and work from home, or DS was at home on study leave. If I had to look after sick children, I would lose a day's pay and have to do a lot of behind the scenes work to make sure my classes were covered.
I think school holidays are a problem for most parents. As a teacher, this is one area where I don't have to worry. However, I would imagine that work breaks over the holidays would be great, especially if you are not the solo breadwinner.