IMO, the problem with creating a white card draw effect is that it simply isn't well-defined. There aren't many white card draw effects, period. Simultaneously, of the ones that do exist, a lot of them have been declared either bends or breaks. More critically, they're almost all one-off effects - we could point to
Puresteel Paladin and
Sram, Senior Edificer indicating that 'cast an equipment = draw a card' is a valid white ability.... but unless we see another card with
Mangara, the Diplomat or
Alms Collector's abilities, it's hard to say that those cards aren't bends.
Another issue is that there haven't been any effects established at common or uncommon - white card draw is pretty much always rare or mythic. I'll also note that almost none of white's existing effects allow it to actually go up in cards - stuff like Puresteel Paladin, Sram, and
Kor Spiritdancer simply make a subset of cards cantrip. It's possible to go up in cards by stacking those effects or using recursion, but they don't refill your hand by themselves. I'll note that even
Dawn of Hope arguably needs a card investment - it does self-enable by generating tokens to draw cards with, but given how expensive those tokens are (and their size meaning they'll rarely live through combat), it's clearly intended that it will be triggered by using other cards to gain life.
Anyway, saying 'I want to design a white card draw spell' is sort of like saying 'I want to design a red lifegain spell' or 'I want to design a black enchantment removal spell' (well, until that was actually added to black's color pie....) - it's simply not well-defined what that would even look like.
....that said, I would say a hard no to
Military Genius's
Military Intelligence effect - it doesn't require any expenditure of resources, and it's already established that is a blue / green ability (since it's effectively a
Curiosity effect). The second effect is a maybe - Dawn of Hope suggests white
might be able to draw cards from lifegain, but it's unclear whether that is actually the case, or if the card is a bend.
Looking at Mangara and Alms Collector, I would hypothesize that punisher card draw is in white's color pie - in other words, it's possible to draw cards when your opponent takes a preventable action. Your opponents can trivially deny you the cards by just not attacking with multiple creatures / casting multiple spells / drawing multiple cards. As a result, I would say that
Tactful Negotiator's ability
might be in white's color pie, since, again, your opponents can negate it by just not drawing extra cards. However, again, it isn't well-established whether Mangara and Alms Collector are bends / breaks or not.