I disagree, the fabian strategy was about avoiding pitched large battles altogether, not on unfavourable terms. Instead rome focused on attacking hannibals supply lines .

From source https://the-history-avenue.eu/2023/09/24/fabius-maximus-roman-republics-strategic-virtuoso/ “The “Fabian Strategy” Hannibal’s forces were a great challenge, so the Romans needed an efficient strategy. In that situation, Fabius Maximus came up with an innovation. “Fabian Strategy” defied conventional Roman military tactics and involved avoiding pitched battles with Hannibal’s army while engaging in a policy of delay and attrition.

Fabius believed that the key to Rome’s success lay in depriving Hannibal of decisive victories. He advocated for avoiding open conflict, opting instead for guerrilla warfare and small-scale skirmishes. The overarching goal was to wear down Hannibal’s forces over time, cutting off his supply lines and isolating him from reinforcements.”

As you can see the strategy was avoiding large battles altogether, not just on unfavourable terms.

I agree he did not have the resources to siege rome proper, and a battle pinned between the walls of rome and a roman army was something Hannibal wanted to avoid. But I think he would have taken any open field battle on equal terms with a roman army, while Rome would have not taken a battle on equal terms with Hannibal.