i can't remember where it came from, but someone, somewhere pointed out that bruce wayne is actually batman's alter ego, not the other way around. bruce wayne exists specifically to fuel batman's ability to keep being batman. i think a lot of it came from kevin conroy in the animated series. He was the one who came up with the "batman voice." adam west's batman was just a little more stern, if anything, but kevin conroy made the voice a distinct character. so when you'd see batman by himself in the batcave, or with alfred, he'd still talk with that gruff voice instead of the soft, higher timbre'd bruce wayne voice.
it's sort of surprising that ben affleck's batman is the one that came the closest to protraying that. bruce wayne only exists to get answers for batman in public. i'm absolutely okay with bruce wayne being around and active as long as that idea is portrayed. when he says "I'm Batman" it's not a silly catchphrase. he IS batman. bruce wayne is the mask.