Based on https://www.alaskaair.com/content/travel-info/baggage/checke... it seems like that would be just two checked bags (not two extra bags, two bags!) and is irrelevant of your seat class? Be lucky the poor bloke didn't need a third bag, that's when it gets really expensive.
I guess I just have to chalk this up to yet another case of oddities in American flights I can't relate to.
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.
For example, if you have the Alaska credit card you get a free checked bag for each of up to 6 people on your reservation.
It sucks that they gouge infrequent passengers, but if you fly even a couple times a year the perks are worth the card fee for whichever airline you fly most.
Also, international flights often do have free checked bags regardless.