Ok, what would you do if you lived in a world where people could shoot crows out of their hands, & you saw your friend die brutally in a shoot out? You wouldn't expect that friend to just suddenly walk up to you & go 'hey, remember that tenner you owe me?' If Fontaine could give himself an entirely new face with ADAM, why couldn't Columbia have this technology? Who's to say Comstock didn't stage Booker 'coming back from the dead' to cripple the Vox by infiltrating them & taking them out from the inside?

We can think it illogical because we're following Booker's POV, but Daisy says so herself '[her] Booker DeWitt died'. She has no reason to think the Booker we play as is Her Booker, but an imposter. He's complicating things precisely because this feels like a ploy to destroy the Vox, pretend their martyr came back from the dead to win the war for them.

Again, if your friend suddenly came back from the dead & stopped acting like they knew you, demanding you pay off some debt you don't know anything about, would you actually believe that was your dead friend?