Choice implies forseeable consequences.
no, it doesn't. obviously in your case it didn't. you've chosen to do what hardin wants you to without knowing the consequences, likely by just taking his story as granted.
but, whether or not, we often make choices in our lives, expecting no or different outcomes, when the reality turns out to be different...
I completely disagree with the assertion that it was clear in advance that Hardin was too hawkish to be reasoned with,...
to me, he had the typical troublemaker attitude from the get go. somebody who's setting up political intrigues to seize power is never to be trusted, but that's just me.
you could very well have a bad feeling about this hardin guy, even at the beginning, not knowing where this would lead to.
Both factions are presented as opponents of the Legion.
no, the brotherhood hasn't had any business with the legion yet. they've been bunker dwelling for quite a time. of course, CL is not the type of organization the BoS would get along with well, but so far, there's no open conflict.
caesar wants them away because of his fota past, true. but for the time being, this is a one way thing.
from hardins perspective it sounds pretty reasonable to let the other factions weaken each other, and then to deal with what is left
Other factions could be reconciled (with a similarly nasty past relationship approximating that between the NCR and Brotherhood) based on their mutual distrust of and animosity towards the Legion. I definitely did not expect to forge long-lasting, best-friend-forever type relationship between the two, but I don't think it was unreasonable to expect that a temporary pact could be formed - or that, at the least, it would not be necessary to kill off friends and potential allies in order to combat the Legion.
i understand your disappointment, but the option was there, just not under every circumstance

if a different a bos management wouldn't lead to different politics, what would be the point of the whole thing?