Not sure if this would matter since airlines can just raise fares by $50 or whatever they would otherwise charge for the additional bag so that customers can still have 2 "complimentary" checked bags.
LAX
Well that can have a pretty big impact. Most carriers now charge $70 each way for a second bag. If that were to be added into the price of a ticket, it would make their fares a lot more expensive compared to AI/9W, especially for pax who wouldn't utilize those allowances. I know this is just an anecdote, but in recent years, my relatives, who are non-elites and tend to just book the cheapest fares, have opted for LH and simply reduced the amount of baggage they take with them. $140 buys quite a bit in India, so no need to take along so much stuff. If LH et al. are forced to allow 2 bags/pax it will bring their prices up in line with AI. So, in the end, while it may lead to more baggage allowance, it will also lead to higher fares.