Delay the Inevitable is generally not very good in ordinary . The most reliable way to trigger the card is through an enemy attack, which Dodge does a better job. Sure it can cancel damage/horror from encounter cards, but there is no guarantee that you will draw those treacheries. The 2 resources upfront + 2 resources upkeep cost could also be painful. It has some use to protect a near-defeat teammate (literally delaying his/her inevitable death :D), but that is not a scenario that comes off too often in my experience.
That said, the card is oddly useful in the 3 Circle Undone investigators that can use it, in interestingly different ways.
Carolyn Fern has better econ to use the card, and has less chance to need to fight an enemy so Dodge is not as useful. Also, if you use her replacement cards, Delay the Inevitable can help to cancel the direct horror from To Fight the Black Wind, thus prevent the doom to be placed on the agenda.
Joe Diamond like the card in his Hunch deck. It is a 2-cost fast Insight, which is just perfect for the Hunch deck. It becomes essentially free (outside of opportunity cost), that you can play it with ease, and not be too afraid if it whiffs.
Diana Stanley may want the card as an additional cancel to fuel her ability. Part of the card's cost is mitigated through her ability. Note that Diana's ability only activates when the card actually cancels something, so the partial cost reimbursement is delayed. It usually is a downside, but it may be useful to trigger Diana's ability out of phase. Certainly worse than Deny Existence though, but Diana may nonetheless want both.