Most people have a steady stream of dopamine and serotonin to help combat the tragedy of suffering in life. If there's an interruption to that supply, or if the suffering overwhelms your capacity to deal with it, prescribed drugs are a logical choice.
Peterson said life is suffering, he didn't say it was a good idea to embrace it or wallow in it, or take a masochistic pleasure in it. He should have read up on the side effects of benzos, but instead he trusted his doctors and that turned into a mistake. Again, he turned out to be one of the 1 or 2% susceptible to the debilitating side effects, and nobody could have predicted that. Not that benzos are good for you anyway, but most meds offer some kind of trade off. We just count on our doctors to estimate when the cure's side effects will be better than the disease.
I've had similar objections, but on examination, he never over promises the consequences of following his rules and he never contradicted them in his conduct. His advice isn't about eliminating suffering, it's about reducing it, and finding meaning in it.
Rules like "Do not let your children do anything that makes you dislike them" doesn't prevent them from getting RA. It helps you teach them how to be kind and tolerable to others while they are being treated for RA. "Set your house in perfect order before you criticize the world" doesn't mean the world has not earned criticism. It means you have to take responsibility for the problems inside your own control before you tackle the ones outside of it.
In the end though, it's up to you. I think he's a smart guy, but that doesn't make him right. I believe he's admitted he sometimes feels like a fraud. He's been incredibly transparent, there's hours and hours of footage of him, and he's a sensitive guy, prone to the same doubts and inconsistencies as anyone else. He just chose to do all that in public, which to me is a questionable choice, but he felt he had to do it like that to maintain personal integrity with his "Tell the truth" rule.
I also think his fanbase acts like a cult, and while I detect no racism or misogyny in him, I see it in some of his followers.