Really, a minor annoyance. Since this has now been the case for a few years, I've ended up learning my AAA number.
Also, you can always put the number in a text file (using NotePad or whatever) and just cut and paste it from there if it's too difficult to remember the number.
I wouldn't avoid Hilton HHonors just because of this -- I've found that ALL the (several) hotel chains I've used have glitches or annoyances on their websites.
In fact, within the last hour I was trying to book a stay on the Priority Club (Holiday Inn, etc.) website and ran into major problems -- their website usually works well but at the moment it seems to be a sick puppy!
So if you're the type that throws hissy fits and refuses to use a hotel chain because of something this minor, sooner or later you'll run out of hotel chains that you can patronize.