Nothing in that proposal violates your objection, though.

They're not saying that people would abandon their daily schedule in favor of one that matched the schedule at GMT. Rather, the number attached to the local time would simply change to match.

It'd be utterly bizarre at first, since there'd be no understood "wake up at 6 to 8am, work through the rest of the am hours into the mid pm hours, head home at 4 or 5pm, etc ", but it seems like once you adjusted to it in your area, it would work.

For example, in my area, I'd be waking up around noon, starting work in the early afternoon, through the pm hours, finishing up around 9pm and coming home to have dinner around 11pm or 12am, and heading to bed in the early am hours. I'd still be waking up in the morning, working through the normal office hours of the day, returning home in the late afternoon, having dinner in the evening and going to bed a few hours later, at night...it's just that the numbers on the clock assigned to those times of day would be different.