It may be difficult, but that is not the issue. One might have to rely on the average price across the day or some other similar metric. Courts do that all the time.

More to the point, if things got really nasty, AA could easily assert that OP broke the contract and that the proper fare was the best available fare at the time he broke the contract, e.g. when he no showed for the second segment.

All of that is avoided by AA achieving its goal which is deterrence in favor of future revenue rather than an add/collect for past frauds.