Pretty sure he was under orders to take the ship out then; it wasn’t his decision. Whomever gave him those orders was at fault; Harriman wasn’t. He did nothing wrong, unless one counts trying solutions we’d never heard of to which Kirk shook his head sadly and didn’t work, after which Kirk tried solutions we’d never heard of which did. That a “because the writer said so”, not any fault in character. This is like people blaming Deanna Troi for the D under Riker’s command being damaged in battle and not subsequently defying gravity.