The basic answer to your question is because customer protection is a lot lower in the US so they can. They cancel, reinstate, and as long as they do that with enough notice they are able to simply accommodate people on their existing/remaining flights without much hassle.

Having said that, the situation you describe of needing to spend days in airport hotels or moving date is most unusual and I can only echo the suggestion to never rush into accepting a rebooking because a cancellation may well be followed by the reinstatement of a new flight within minutes of your initial timetable within a few days. I don't think I've ever had to suffer an unwanted change of date due to AA cancellations in (literally) hundreds of cancellations over time, especially given the profusion of AA connecting points etc. As noted by others, the upside is also that it gives a little flexibility if your initial timeable was not ideal though with BA, things have become a lot more restrictive over the years (for instance, it used to be the case that you could easily change the whole itinerary, now they often insist on your only being able to change the part of the itinerary that was affected by a cancellation etc).