Every 747 pilot landing at LHR does that. Yeah............ they carry the AIP for every airspace they overfly.
They don't have to carry lots of books. In most cases they will not carry full Jepp coverage either.
Airlines have an ops department that in some cases produces their own charts and in other cases uses a 3rd party eg Jepp to produce the charts that they use.
Either way what we are talking about in an Airline / AOC operator's case is Part C of the Operations Manual. That document is inspected approved and audited. An airline / AOC operator will invest more money and time in establishing a proper relationship with their chart supplier than the average private pilot.
You seem to forget that an airline does not wake up in the morning and say "let's grab the Jepps and fly to somewhere new". A new route or a new area of operation involves a lot of research, consultation, training and approvals.
Airlines are not only interested in the accuracy of the data they also get quite involved in the AIRAC change-over times for the various databases. You may not have realised it but while AIRAC changes happen at midnight (ish) most databases change over at 0900z on the AIRAC date. This means that if you are in Europe, departing at 0500 and arriving at 0800 the database will not be updated.
In this case, Airlines and AOC operators will have measures in place to ensure that the pilots are aware of any changes and the flight complies with any changes that may be in the system.
Overnight flights from far away also have to be aware of this and have measures in place.
So while Airline pilots may not have the AIP under their arm, they are accutely aware of many more relevant AIM aspects than you seem to be.
Finally as an example, it takes less than a minute to check what changes are happening in the UK on 16 December (Next AIRAC date). Having done that one can sit back and wait for the new Jepp charts to arrive. If they don't arrive then one is still aware of what is changing and can cope. Same thing can be done for every other European country. Not very hard now is it?