I don't think people use "second unit" literally.
Props to you for recognizing that it's a myth. That was my point. I guess the next step is that we drop the term in favor of something that fits reality better. I’m not holding my breath.
But the argument by some fans that this "second unit" needs a scorer suggests that others do not use it literally.
That said, our leading starter (Kyrie) played 32.2 minutes per game last year, with the other starters in the vicinity of 30 or 31 minutes. We're going to need roughly 80 - 90 backup minutes per night.
Or indeed less than that. But of course it's guaranteed, unfortunately, that front line players will miss games, so a whole "second unit's" (!!!) worth of players may hope to average rotation minutes, as they did in fact do last season.
What you say about the starters is true - but of course even the term "starters" on the Boston Celtics is a bit mythical as well. Because if you literally mean "the players who start the game", then you'd have to include Baynes, who averaged only the 9th most minutes on the team (8th if you don't include Greg Monroe) per game, but who started 67 games - and who seldom got crunch time minutes; even Ojeleye got more.
And if that's your definition of "starters", it's arguable how meaningful that term is, either. As I recall, it was Red Auerbach who said, "It's not who starts, it's who finishes." (If not, it surely sounds like him.) So maybe we ought to start talking about "finishers" instead of "starters".
A modest proposal.