Perhaps so. But it is hardly a strategy to chase Spirit out of DFW and then do nothing. Low oil is not here to stay and AA knows it. Saudi's budget deficit for 2015 is predicted to be $107 billions by the IMF. This article shows each country's break even price to balance their budget. For Saudi it is around $105/barrel.

Break-even oil prices for all the major producers in the world - Business Insider

At this rate Saudi is predicted to run out of money in 5 years. I doubt they will go all the way. Not to mention Saudi is not the only one with a deficit. Other countries running out will destabilize the region even more. It is already happening. They can close the pipe tomorrow. It is up to them.

AA would be stupid to just make a short term move. Oil will rise once again and we will be back asking for more gates. Killing or cannibalizing Spirit and Frontier both is certainly possible. But it is not a solution. Another Spirit will pop up the moment oil is back up. The long term solution is to create a sub-brand or shift the brand and enter that market.