I think the general analysis of Grace in fandom glosses over one tiny little nugget (two, really):
Grace didn't say "don't send the mission, let everyone on Earth die so I might live." Grace said, "send the mission three months later after I train someone else who will actually succeed and wants to die." STRATT was the one who said that casualty estimates go up "exponentially" if there are any delays, so she didn't want to wait.
Let me repeat that for emphasis: Stratt sent their BEST EXPERT IN THE THING KILLING THEIR SUN in a potentially-fatal coma to bumfuck nowhere, Space because she didn't want to wait THREE MONTHS for him to train someone who was NOT their best expert in the thing killing their planet to go.
I don't blame Stratt for her decision-making paradigm because Grace hadn't done any of his really cool shit yet.
However, astrophage is supposedly impenetrable. However, taumoeba has to lyse astrophage to eat it and is not lysed by astrophage in self-defense. We literally watch it happen on screen.
Grace, in the book (they don't go into this in the movie) figured out how to lyse taumoeba so he could eat it, in somewhere between one and three years. So it is entirely possible that if Stratt hadn't wasted Grace on a twelve-year (non-relativistic time) coma, he may have figured out how to lyse astrophage on his own.
He never even attempts that line of research in the movie canon -- they task him with breeding and testing astrophage, then immediately yeet him into the void upon completion, and he's working on figuring out Tau Ceti's deal immediately upon waking -- so we don't know how quickly he would have figured it out. It could have been in the one to three year timeline of lysing taumoeba, or potentially longer.
Either way, that means that to save three months' of casualties, Stratt may have spent somewhere around twenty years' of casualties. (It took twelve years for the Mary to get to Tau Ceti, six months for Grace and Rocky to figure out Taumoeba, twelve years for the beetles to get to Earth. We don't know how long it would have taken Grace to figure out the chemical compound that lyses astrophage on his own, but the excess casualties are (the twenty four years and change it took to solve astrophage in the canon continuity) minus (how long it would have taken Grace to lyse astrophage).)
That is a bend over a dollar to pick up a dime situation if there ever was one, not that Stratt had any way of knowing what Grace would ultimately be capable of beyond the general principle that it's a bad idea in war to use your general for cannon fodder.
Stratt also had no way to know that Grace would magic food out of taumoeba, and could magic food out of fucking taumoeba. But if that man had been back on Earth with an actual CRISPR and more to work with than one space amoeba strain, her starvation problem also might not have been as bad.
But we will never know, because Stratt would not wait three months.
... I would feel really bad for Replacement!DuBois, in that scenario, to wake up alone on the Hail Mary and the Earth's sun is already at luminosity.
... OTOH, that does lead to the potentially hilarious solution for Rocky of packing the lone human up on his ship and heading off to Earth so his new leaky space hitchhiker roomie can ask on Erid's behalf what the fuck the humans did, since figuring out the Tau Ceti thing has been nothing but a bust.