I just looked up a flight, for example London to Paris. The cheapest BA ticket includes hand luggage for £57 each way, or the next option with checked baggage is £14 more.
I'm sure there probably are cheap-and-shit airlines that include nothing with the ticket price as you mention, but there clearly are also options where you pay a small fraction more (and certainly less than "additional baggage" charges) and have baggage included.
And you framed it as if every American airline charges extra for any baggage of any kind
I didn't proclaim "American airlines charge you extra" did I?
The latest innovation of low cost airlines, as of a few years ago, is to charge for even the hand luggage in an overhead bin. You can only take a really small bag which fits under the seat in front without paying. BA haven't yet got to that level (although I'm sure they will with time). BA tend to be 30-50% more for the base ticket though - so you pay for it one way or another.