Yeah I found that a bit strange with the clips i've watched myself. I recall watching a clip of one girl repeatedly breaking the rules and going on to have someone get her microphone before chucking it in the pool. There was no "this is Big Brother" it was like "oh its Allison".In the US version on air you rarely if ever heard the "voice of Big Brother". If you watch the US live feeds, they typically just had pre-recored messages, or they would cut the live feeds and just yell out instructions to the houseguests. And the houseguests would alway refer to the production team, not as Big Brother, but as "them" or "they" or "production" or at times they would even use the specific names of staff members.
As an Aussie, i've only watched all of AU and a majority of UK seasons, and yeah there is a curiosity about the person matching the voice, but in BBAU from early days to 2014, we did get to meet the main ones and even then, they usually had a certain voice to distinguish themselves as BB vs themselves.