Better would be incinerate the body so Shepard's corpse doesn't become a lab experiment, then someone's pawn, helpless and at the mercy of Cerberus's whims.
Liara giving the body to anyone and walking away as though she has no responsibility for what happens next is unforgivable.
BW involving her in that plotline does Liara no favours and honestly it works just fine without her.
Except, again, she doesn't just walk away and wash her hands of it. Her work after this is dangerous and it is centrally focused on finding out what happened in spite of the danger, and then working to take on that power and come out at an advantage. There's a reason she doesn't tell Shepard right away, and a reason she keeps Shepard kind of at a slight distance even though it's not what she might like (especially if you were in a relationship).
She always maintains a connection with what happened, her role in it, and works another angle. The Shadow Broker was involved too and she's clearly spending time keeping an eye on multiple things, as well as working carefully to untangle others.
She's entirely plot relevant and no, the intricacy of what she does in all of this wouldn't have done without her. I was bummed she wasn't in my squad, but truly, given her personality, her background, and her knowledge, she was the perfect person to do all of this.
Either way, I'm getting off this now, but for a Solas comparison - he too has multiple things going on that aren't truly revealed for some time, but hinted at. I think that kind of depth, and that perserverance are compelling. Solas woke up to threats, danger, and upheaval. It was sad and seems to be appalling to him, leading to negative experiences even as he continues, determined to help, even though whatever his plans are might have terrible circumstances.
Essentially, it's risk taking. As I said, most of the original crew gave up and split up. Liara took a risk that could've ended badly, but this was the lesser evil, so to speak. More of a known entity. Solas seems to be preparing to take a risk too, and it seems that could also have a chance of going badly (and he seems to believe something will be going down as a result).