I haven't gotten that far in the show, but in the novel Leviathan Wakes, it's explained that
They can't just blow up Eros because that would scatter the protomolecule throughout space, making it impossible to prevent Earth, Mars, or, well, anyone from getting their hands on it. They need the Nauvoo not to destroy Eros on impact, but to use its incredible thrust push Eros into the sun, which they are confident will actually destroy the protomolecule.
Here's the transcript from my hard copy of the book, apologies for any typos:
"Even if we studded the whole thing with nukes, how would we be sure that no little scrap of the thing would make its way to a colony or down a well? Blowing that thing up would be like blowing dandelion fluff into the breeze."
Miller has never seen a dandelion, but he saw the problem. Even the smallest portion of the goo filling Eros might be enough to start the whole evil experiment over again. And the goo thrived on radiation; simply cooking the station might hurry the thing along its occult path rather than end it. To be sure that the protomolecule on Eros never spread, they'd need to break everything on the station down to its constituent atoms...
"Oh," Miller said.
"Yeah. You're not going to like this."
"Okay. You asked. You need to drive Eros into the sun."
"Into the sun," Fred said. "Do you have any idea how much mass we're talking about here?"
Miller nodded to the wide, clear expanse of the window, to the construction yards beyond it. To the Nauvoo.
"Big engines on that thing," Miller said. "Get some fast ships out to the station, make sure no one can get in before you get there. Run the Nauvoo into Eros station. Knock it sunward."
"The Mormons are going to be pissed."