I really do feel like the movie gives u this idea that Grace is and has always been a coward prior to boarding the hail mary but. in the book you get his internal dialogue. and its not so much that he is a coward, its just that he is very not self aware of his own place in the world. he doesn't elevate himself at all.
he's surprised that anyone would want his opinion on the astrophage after being ridiculed in his field, but scrambles to stay in on the project once he realizes how dire the situation is and how half of his students would likely die in the next 30 years and wants to be a part of something that could change or prevent that.
but throughout the project he's constantly being dragged by strat to meet new hires for the project, he is there to converse with and help vet every. single. person. who is hired to help work on their only chance for saving the sun and the entire planet. and he has to be Told that he's essentially strat's second in command and he still hardly wraps his head around it.
he's given important things to check over before launch and thinks its just shoving him in a corner to do bitch work but it is a VERY important checklist that ensures the stability of the ship and mission.
they have him walk underwater in a pool to use lab equipment to mimic the zero gravity experience. he knows the most about astrophage and everything they've done to breed it and make a ship that specifically runs on it for fuel. the spin drives, the capacity, etc. and he does do training. he is quite literally mission ready in the novel.
his problem is he watches Strat by his side for years and sees how she pulls people in without hesitation, and accepts the inevitable fate of everyone, going so far as to make sure the team has backups with the same training in case of an accident.
Grace knows she works like this, and nothing has stopped her make difficult decisions or override international law, and his problem in the end is that think he's safe from that.
he does not consider his importance, the value of his knowledge, he barely processes how his peers view him. his problem in the end is not that he's a coward, its that by undermining himself he never once mentally prepared himself for the possibility of having to step in and be on that ship. he does not think he'd be that important. that valuable.
he still doesn't want to die; he doesn't want to go. he does spend 3 hours deciding he doesn't want to do this and tells strat as much. tells her to send the one willing scientist left in the world but very quickly finds out its not about who is willing, its about who can do the job.
and he can. he is truly the best candidate for the job. there's no way they could send anyone else.
if he only knew his worth, or acknowledged the value he has among his peers, he would have considered the possibility it could be him if something went wrong a long time ago. he could have mentally prepared for that and spent those 3 hours accepting it, however miserably so. he would have known it could only be him as soon as he processed the other mission ready scientists were dead.
but that's not the kind of person you get after they wrote a speculative paper that was shamed and ridiculed enough to drive him out of his field and into a job with much less peer review, and never once attempted to crawl out of that safe space he made for himself. never once considered stepping back into his field and standing his ground.
you don't get a hero who rises to the challenge when they don't even consider what they have to offer has value to someone else, enough to save their entire world.
grace is not really a coward.. not like that. he just values himself too little.