Like I said, the biggest problem should Stephanie’s own child be retained (or where Stephanie has to look after her sisters’ nieces and/or students) is that she might nag at Tim whenever he lazes around. Actually superheroes being nagged at isn’t unheard of. Iris West does it to Barry Allen. Even Jean Grey nagged at Scott Summers when he looked at Psylocke. But in Tim’s case, it’s more like that nobody wants him to be depicted in a bad light and partly why some people take issue with Iris (whether if she’s black or white).
If because nobody wants a woman barking orders at a man and the like. Actually Stephanie did nag at Tim Drake before. However with a small child around, she’d probably be so stressed out that she needs Tim to help her. If he doesn’t, she’s going to get really frustrated. (I also think if Stephanie’s child were to be retained, she’d probably end up as a working mum to support them and herself, which’s also unprecedented if you observe the early Spider-Man stories.)
If Iris West’s any indication, should Steph ever nag at Tim whenever he screws up fans wouldn’t like it. Especially if/when said character’s supposed to be an audience surrogate (Barry and Tim) that it wouldn’t be fun seeing their girlfriends constantly nag at them for screwing up in some way. (To be honest, Iris didn’t seem that dark-haired before in the earlier comics and she’s what Steph’s like if she were older or at least allowed to be more independent*.)
If Stephanie initially showed up as Tim’s sidekick, her nagging at Tim for screwing up and demanding him to help her raise the baby or do household chores and looking after children together would lead to an uncomfortable role reversal. In the sense that Steph orders him around to help him do domestic/familial duties though that would be implying Steph’s portrayal in the older stories tend to be paternalistic.
In the sense that the possibility of her being better at somethings (like sports and even coming up with her own gym equipment) wouldn’t just be emasculating but also not a good look for Tim if he’s supposed to be unathletic. Her portrayal being paternalistic now makes much more sense with stories where somebody tells her to give up the baby (never mind that she could end up being attached to them if she cares for them a lot) and her not being trusted around.
Especially when it comes to training her (though some of it’s secondhand so). If true, it would be highly uncomfortable for fans to have her nag at Tim for not helping her around in looking after the baby/babies and house. It would be just as uncomfortable if Steph’s shown to be a working mum if because that makes her much more independent than initially portrayed.
Seriously, she wouldn’t always have much time to date Tim and when she does, she also demands Tim to help her with the chores which would put off audiences if because they’re not used to these portrayals. Though that would deconstruct just how misogynistic Spoiler was portrayed as and still is.
*Initially and for the longest time, Iris wasn’t Barry’s sidekick let alone a female Flash since that belonged to Patty Spivot in the older stories.