I mean, she's an elderly oligarch who (from what I understand) wouldn't have been terribly upset with the whole "raksha husband" thing beyond its impact on the House's reputation
I mean, I'm not going to go into her exact reasons, but I can confidently say that if Inks had told her about that and proven it, Bana would have
hit the fucking roof and probably sent a fully-armed Iblan legbreaker squad to bring her granddaughter in for a thoroughly unpleasant "talk". And as for "without causing any disruption beyond the bare minimum"...
... yeah, no. Sorry, but, hahah, no. I'm not going to deny that Inks is indeed reforming the plutocratic oligarchy to be less horrible, or that Gem as a city will likely end up wealthier for it and a more pleasant place to live for the average resident... but "without disruption"? No. Just by the very fundamental nature of what it is that she wants, Inks is going to wind up toppling the Great Houses in their current form,
ripping apart the economic system of slavery that Gem is built on, unseating pretty much everyone currently on top of the heap
including the Despot, and probably causing a decent-to-middling population turnover. It'll be a richer, fairer, nicer place to live afterwards, but even with Solar Charms in play there's going to be chaos
during, and a lot of the people currently benefiting from the way it's set up (some of them relatively blameless, insofar as any non-slaves in Gem are) are not going to be
around "afterwards", and certainly not in any fit state to appreciate it.
Bana isn't a blameless saint here, or even really in the right (well, except the political right, lol), but don't try to act like Inks isn't two short steps shy of an anarchist revolutionary in how she wants to utterly rewrite Gem's political and economic landscape from the underground up.