It's true that we actually probably didn't need to be involved in the events of CT as they happened in ARR.
However, the fact that we were involved means that those events as remembered by the Exarch did unquestionably involve us, so they cannot happen without us.
Yes and no. Forcing completion now during 2.X is logical because that is clearly where the story sits in the wider scope of the plot. Cid is in his ARR outfit before he gets a new one during Heavensward; Nero is fresh from his defeat at the Praetorium; the recent destruction of the Isle of Val (established in 2.X MSQ) was referenced.
I do agree there should have been an additional gate placed at the end of 4.55 to catch players who were inbetween 2.5 and 5.0 at the time the requirement was introduced, instead of leaving it right until 5.3.
(throws spoiler tags to the wind at this point)
I do actually agree that 5.3 would have played out better and more in line with the overall themes of Shadowbringers (nothing should last forever and there's a beauty in man's ephemerality) if the Exarch had truly died – but that wouldn't have precluded us still waking up young G'raha afterwards, just not as an alleged continuation of the same character we'd been dealing with throughout 5.X.
(My preferred take would be that the Exarch died without passing his soul into the vessel, so we could still pass his memories but not soul to young G'raha and everything would play out much the same since then – except that G'raha would be talking about the Exarch in third person.)
All that said, even if they'd simply closed the loop and had the Exarch die, without us waking up his younger self at all, the writers may have still opted to force the storyline simply because it does give that critical context to Shadowbringers and while some may be frustrated by it, on the other end there are people who are disappointed that they had no idea that they should have played it first.