I don't have status with American, but have a p big status with United so can speak a little to it.
Your home airport is LAX right? Getting free upgrades out of a hub can still be tough because you're competing with the business travelers. If you're trying to take a Monday morning or Thurs/Fri evening flight in or out of airports like ORD, LGA, JFK, DCA, etc. your chances of getting upgraded are going to be slim to none. There will be a bunch of people with executive status or whatever ahead of you who aren't going to get upgraded on those flights.
It's still very worth it to have the status though. If you're not planning to fly during peak business traveler times and you're not going hub to hub your chances of getting upgraded aren't non-existent. Maybe 50/50, but it's not super predictable. Getting upgraded at least to the premium economy seats is still pretty common though.
The best perks of having a high status, imo, are free flight changes and the lounge access. When you're stuck at an airport and your travel plans go tits up because of weather or other flight issues you're way more insulated from having to deal with the same bullshit as everyone else. They'll do things like hold seats for you on multiple connecting flights and stuff that they won't do for the general public either.