(3) show who? In the sad reality where these jobs are very attractive to predators/paedos who want to gain access to kids, I’d rather not use my own precious children as ideological Guinea pigs to prove some point about gender equality.
You're showing the whole of society - including the tiny little kids who are in the nursery. They don't just exist in suspended isolation, as primitive creatures who are fed and have their nappies changed and nothing much else - every second of their lives, they're learning and absorbing so much.
Nobody ever says that there's no point in adults talking to or reading to little ones, on the grounds that they cannot yet talk or read themselves. We could just wait until such time as they can talk and read on their own... and then be surprised that that time never arrives - as nobody has ever modelled or introduced them to it beforehand in those crucial first years.
We start off with tiny children who only know women as carers - especially those from households where no adult male lives. This cements it even in their young minds that men have no meaningful role in caring for children. Some of them probably find it a shock if they get to primary school and find that there are actually men there in loco parentis.
I wonder if this is a contributory factor in many of the useless men who've always assumed that men are free agents whilst women and children come as one combined package. Women are great for sex, but if the worst comes to the worst and they have babies that you can't be bothered with at any time, you can just leave that mother/child combo and move on to another woman with your time, money and efforts.
Meanwhile, those girls who have also grown up with exclusively (or near enough) females looking after them end up as women who may express horror at the very idea that men could want to work with children and be declaring that there must be something inherently wrong and untrustworthy with all of these men.
Remember: there was a time when nobody - of either sex - could possibly understand why a woman would want to drive, work outside of the home, bother her head with adult financial responsibility, vote etc. Where did they get these preconceptions from, if not from having grown up in a society that instinctively taught them this from a very young age?