I'd support her to listen to her solicitor, TBH. But I think she should also weigh up the costs (emotional as well as financial) of getting into what might become a battle.
My situation isn't anything like as polarised as your sister's, but I would say: parents who were happy for the other parent to do the lion's share of parenting while they were together don't suddenly change. I'm just over two years on from splitting up with my ex, and there is still a constant stream of silly questions, last minute requests, and helpless 'oh goodness I can't find a school jumper, what can I do?' type texts.
I just keep a firm line. I ensure my DD has what she needs, and if my ex cannot get it together, it is not my problem.
And I don't think my ex is as hopeless as most men, especially a man who's relied on his partner as much as it seems your sister's partner has!
It would not at all surprise me if the 50/50 idea turned out to be very short-lived.
What your sister does need to be careful about (as a PP says) is getting clarity that if they are doing 50/50, this also means splitting the cost and the organisational faff of clothes, equipment, clubs and activities, etc. It doesn't sound as if they're there yet, but if they do get to a point where they're doing this relatively amicably, there is a Cafcass plan you can fill in, and it allows for lots of detail, so you can specify things like 'we will take turns to buy school shoes' or whatever. That means he needs to step up and do the boring bit of sitting in Clarks, not just shelling out money.
He may realise this is not so much fun as he imagined.