I agree with the above, but for possibly a different reason. And my understanding may well be wrong, but...
If you're in an accident and are at fault, surely that's where the agreed value comes in? It most possibly won't cover all you've spent keeping the car, or replacing like for like. But you'd have an amount that you could do with as you please. You've mitigated your risk to a degree by having the insurance at a value exceeding minimum market values.
If you're not a fault then surely you've got legal recourse to be put back to the same position you started (whether that's financial or otherwise). So if the party at faults insurance couldn't provide an equal replacement then rebuild and repair should be on cards. And if the car isn't salvageable then the above is likely all moot anyhow