You have answered your own question by providing the official reason Ryan Air do this: to ensure compliance with immigration authorities
When Ryan Air first introduced this policy in 2009, they claimed:
A Ryanair spokesman said it had introduced the rule early this summer
to allow non-EU and -EEA passengers to use web check-in. Previously,
the airline did not allow non-EU and -EEA passengers to check in
online; instead, it offered a refund of the extra cost of checking in
at the airport.
Aer Lingus says it does not have such a requirement.
“For those passengers who check in online, passports are checked
either at the bag-tag desk or bag-drop machine or at the boarding
gate,” a spokeswoman said.
The Ryanair spokesman said: “Other airlines
don’t offer passengers the convenience of 100 per cent web check-in,
so they don’t need to do this yet. They check visas at their
long-queue check-in desks, which Ryanair passengers now avoid.”
Most of the time an airline is responsible for the return flight when you are refused entry at the destination port. All other airlines do some form of basic visa checks in the background. Ryan Air either have not updated to procedures, or are choosing to do it this way.
Another thing to note is that Ryan Air only checks that your Passport is OK to travel, or that you have a valid visa. They don't check for example whether you are overstaying your visa (e.g. the 90/180 rule).
But what about Domestic flights or flights between Schengen countries?
This is where their official reasoning breaks down. They have a blanket policy for all Non-EU Nationals regardless of the flight they are taking. Obviously there is no immigration requirements for domestic flight, nor is there one between two schengen countries. They might say it is easier to have one policy for all their flights, but its hard to believe this when they are the only ones to do this in the first place.
Why don't they just perform the check at the boarding gate? Actually I have witnessed some positive experiences with other passengers forgetting their visa check, and the staff being nice enough to check it and stamp it at the boarding gate. However this has been far less than the experiences of seeing people rejected.
inserted:
From Easy Jet (another budget airline)
Will my travel documents be checked at the airport?
You need to provide photographic ID at check-in on all flights, including domestic services.
On domestic flights (excluding Italy) an ID check at the boarding gate
is NOT required for passengers travelling with cabin baggage only. It
is only mandatory that ID checks are conducted for passengers
travelling with hold luggage. If you check-in online you will still
need to provide your photographic ID when you go through security and
again when you board the plane.
What are the travel documents that I need?
You need to provide photographic ID at check-in on all flights, including domestic services but the types required vary.
For clarification please see the table below:
- not every country issues a national identity card. Please note: a driving licence does not represent a valid photographic ID, with the
exception of UK domestic flights.
Money Making Scheme?
Many people actually (as @Andrew Lazarus has already mentioned) believe this is another one of their money making schemes. Many passengers are denied boarding due to this clause and by that time they do not have enough time to go back to the check-in counter and come back through security to board the flight. Thus requiring them to purchase another ticket.
I would tend to agree with this idea, they also are very strict with the check-in bag sizes and their idea to charge for using restrooms
Update:
I asked them on Twitter about Domestic and Schengen flights:
I was unable to get them to give me a reason for why they do the visa check for Schengen flights
