None of the European compulsory reservation operators do waitlists or standby. That's a US airline/Indian railways practice. Even European airlines don't do it.
British Airways do both wait lists and standby but neither are open to the general public. It's mostly non-revenue passengers who can use them (staff and some executive club redemption passengers) but there's limited circumstances where revenue passengers can use them too, usually after a cancellation or missed connection at Heathrow.
Standby is also used when overbookings happen, those who they intend to bump off the flight get put on standby for the same flight and still go to the gate so that if enough people don’t turn up they’re there at the gate and can still get on - that happened to me a couple of months ago, fortunately I did get on.
Airlines require check in because they still have to check your ID for security reasons on the majority of carriers, and if not still need to know a manifest of whose onboard incase of a crash. They cannot accept walk ups because everyone must legally be seated and have a seatbelt for safety.
The bit about walkups isn't strictly true. BA have always accommodated walk ups to some extent, to what extent that is has varied over the years. At present you can turn up at the airport without a booking up to an hour before the flight leaves and if there's space on the flight you want to travel on you can pay for it there and then at the airport, have your documents checked and go through to departures for the flight. You’d be surprised how many people do that, especially on domestic routes.
Pre-Lockerbie BA had an offer on some domestic routes (iirc Heathrow to Edinburgh, Glasgow and Manchester) where anyone could turn up (with as much luggage as they liked!) without a booking 10 minutes before departure and be guaranteed to fly, if there were more passengers at the gate than there were seats on the aircraft they'd operate a duplicate flight. There was always an aircraft on standby at Heathrow for that purpose, often Concorde which meant there were multiple occasions where a very small number of walk up economy class passengers were flown to Scotland on an empty Concorde! There was at least one instance of a 747 being flown to Scotland just for a single digit number of walk up economy passengers too.
That obviously wouldn’t work on the railway, even if there was a spare train for excess passengers pathing it would be a non starter.
The CAA haven't changed anything; there is still no statutory requirement to produce any form of ID to fly on a domestic flight with hand luggage. Indeed airlines such as Loganair still don't require it unless you are checking in luggage.
Was happened is that the CAA audited BA and found that due to their phenomenally poor IT, they were unable to guarantee that the person who flew was the same person who had checked in luggage. The post-Lockerbie implications of that lapse probably don't need spelling out.
Other airlines are sufficiently competent that they know which passengers have checked in luggage, and can thus limit ID checks to them.
BA's IT system has nothing to do with why the CAA made the ruling that they did. BA’s IT system is as capable as any other UK airline’s IT system of complying with CAA legislation and staff are thoroughly trained before they’re allowed to use it unsupervised - I have first hand experience of using the system and lets just say it’s not very user friendly! But it does what it’s designed to do.
There's two ways to ensure that the passenger boarding is the same one who checked the bag without requiring them to bring physical ID - one method is to use biometrics (the equipment for which is provided by the airport not the airline), the other is to have the same staff do both check in and boarding and therefore recognise the passenger who checked the bag when they board (and have the bag offloaded if they don't board). The latter method can only be relied upon for very small aircraft ie a Twin Otter and even then only at very small airports ie Barra, for larger aircraft and airports the only option is biometrics as staff can't reasonably be expected to remember the faces of 100+ people. The ruling against BA was made because they were relying on the staff recognising people at airports that don't have biometrics equipment. BA would have been permitted to implement the same policy as Loganair but instead chose to implement the policy used by easyJet and Ryanair.
Why the CAA took until this year to make that ruling I don't know, they'd been aware of the issue for well over a decade.