I also thought it was rather callous and unheroic of the characters to go "Yeah, let's encourage him to exert himself and use up nearly all his remaining lifespan" instead of trying to convince him to stop exerting/aging himself so they could help him. The most we got was a token "Don't do this" without any followup.
True, it did seem callous. I can only think that maybe our heroes did not see any alternative. Griffin seemed very unwilling to stand down and Barry did not have his powers. So, they needed to find a way to defeat a man with super strength without using any powers.