Sure, there's opportunity cost, but there are also costs way beyond the time you take fretting over a decision. You said it yourself: You're "crippled" by anxiety. How is that better than making a random decision? Or just going with your gut?
Given the alternatives of either 1) not making a decision, 2) drawing out the decision for a long time, or 3) failing to act in time on the option, simply making a random initial commitment addresses the decisionmaking aspect.
Many decisions are capable of being reversed or changed later. If you're ever in a situation where you must decide (stay or jump from a burning building, say), there's still likely to be an option which is least bad. Even those who jumped from the WTC on 9/11 were making a decision. The outcome wasn't optimal, but in the circumstances, it may well have been preferable to the alternative.
Flipping a coin is a way to think about the "what if I choose option B" in a way that feels like someone else made the decision so it's OK to resist it, instead of feeling like you made the descision yourself and get stuck in consistency bias (stubbornness).