The difficulty is in catastrophe curves. While the water from a single flight doesn't hang around long, there are always aircraft in the sky, so it's constantly getting refreshed and amounts to a constant thermal load. If that additional thermal load, on top of the other greenhouse gases, is enough to tip some nonlinear system past its tipping point, then we've still got a problem.
Fortunately, it's also its own solution: if we find we need to avert a catastrophe next week, grounding all flights today might do the trick. But of course it's very hard to predict a tipping point to that level of accuracy. If we had that sort of movie-plot threat in climate change we might actually see meaningful action.
So yes, while carbon dioxide and methane are terrible, awful, no good gases we shouldn't be dumping into the atmosphere with quite such abandon, choosing to maintain water vapour at a particularly vulnerable point in the system is also something of an unforced error.