When I started work,in the very late 60s,I was a travel agent.In those days airline tickets were written by hand. Airline accounting was largely manual. There were no bar codes involved in the air travel process.
On an IATA ticket there was a box called "Taxes". Very rarely used in the UK it was about the airline collecting a government imposed tax. The USA had an 8% transportation tax on tickets issued in the USA so that value appeared on their tickets but not on tickets issued here in the UK. The airlines identified any taxes as part of their accounting process and paid the government.
Sometime in the 1980s various other "agencies" wanted to collect money from passengers.Typically these were airport fees but the airlines began to balk at including the fees intheir fares.I heard one airline official complain that he had to keep putting fares up just to cover these fees. In the end I think it was the introduction of PFCs (Passenger Facilities Charge) in the USA that broke the camels back. PFCs were intended to cover the cost of building new terminals at US airports. The money wasn't paid to the US government; it went direct to the airport and,as such,it was not a tax in the true sense of the word.
The PFCs were followed by charges levied by government agencies (e.g. immigration) - still not taxes but the airlines swallowed the pill and collected and remitted everything by showing these fees in the "tax" box on the ticket.Eventually it was renamed "taxes,fees,charges".
Only now did bar codes begin to appear but it would be the 2000s before the use of those bar codes started to appear at airports and by that time the whole process of collecting all the taxes, fees, charges was embedded in airline accounting systems and has stayed there.
It's worth noting that many airlines have a two stage accounting process., It starts when the ticket is issued and the detail on the ticket is stored. As the passenger flies each flight so the ticket accounting record is updated. If that flight has taxes, fees,charges the money is set aside for payment. it may also be that the flight was operated by a different airline and that money is put in another pot (airlines then exchange details of such "interline" flights and total up who owes who rather than flight by flight).
What's the purpose of bar codes in airports? It depends where they appear in the process. At the gate it's about checking the passenger is boarding the correct flight. In duty free it'sabout verifying that the passenger is entitled to duty free.Before security it's about making sure only passengers get past that point although I have wondered if the airport might also use it to audit the monies paid by the airlines.