Checking IDs at boarding does about as much to security as putting your toothpaste or your less-than-100ml-portion of Nutella in a transparent plastic bag and put it on the Xray separately.

Let's work logic for the criminals and see which ones you can really capture with that medthod. Let's assume someone has committed a crime and has not already fled the country before being identified and all databases updated (which already eliminates many criminals).

• Let's assume he wants to leave the country by plane. As soon as he makes a booking under his real name a computerised non-fly list would identify him and he could not fly.
• Let's assume his not caught by the no fly list and wants to leave the country to a non-Schengen country. In that case he needs to go through passport control which is done by border police. There he can either i) be stupid and use his real ID and real name on the ticket -> border police will detain him ii) be stupid and use his real ID and a ticket with a false name -> border police can detain him iii) be a committed criminal and get a fake ID and also use that fake name on the ticket -> border police may spot the fake and detain him. Thus, 80% of those cases would be identified by the border police, either because of the name match on the real ID or because of the fake ID
• Let's assume he made it through the no fly list and through border police. He then goes to the gate, where he has to show his ID and ticket. Again, i) real name on ID and real name on BP -> there's no way gate agents can tell he's a criminal -> happy flight ii) fake name on ID and fake name on BP -> there's no way the gate agent can tell a fake ID -> happy flight
• Let's assume he wants to flee to a Schengen country. Easy, take a car and drive across the border, there is no border police and no ID check. However, this being Schengen he can just as well be detained there.
• If he still wants to leave the country by plane: i) use real name -> no fly list, or making it past that see above, he'll be facing gate agents that can neither identify him nor can they detain him (they could downgrade him or lose his luggage ) or ii) use fake name -> same story, gate agents don't know and couldn't do anything anyway.

What this logic shows is that the way to capture criminals is not to have their ID checked against their boarding pass by people who have no way of telling who is a criminal and even if they could tell would be powerless to act. Criminals must be identified, hunted and detained by institutions and people that have the skills and rights to do so. Airlines neither have the skills nor the right to do that. Conclusion: checking IDs at boarding is senseless.

??? Taking passport out of your briefcase/pocket, giving it to the gate agent, who may have to open the passport, find the right page, then will look in your passport for the name to match (not all countries' passports are laid out the same way), then look for the matching name on the BP... 5-10 seconds. Even if it was 5 seconds. Take a planeload of 120 passengers. 5 seconds * 120 passengers = 10 minutes lost. 10 minutes more on the ground for a plane is a lot of money.

Not sure what you mean by "anyway". You do realise that BP and ID are two distinct physical objects? So showing one does not necessarily entail showing the other in the same movement. If by "anyway" you mean "you have to stop at the gate agent anyway" then, also the argument doesn't hold. Either there are automatic self-boarding gates or there is a gate agent, who would merely hold your BP under the scanner at the boarding gate. Thus it's either no stop at all at the gate agent or a much faster operation.

Because of certain events in 20th century history not everybody in Europe has a German ID. Nor a French for that matter. Take a big hub airport like CDG and any flight has passengers from France, the destination country, USA, Japan, some African countries, Brazil, any other European country, China - you name it!

Err, yes, and in other countries as well. But what has that got to do with flying? You mean the analogy is that only certain people are entitled to certain products, such as cigarettes or a certain airfare? Two big differences, one in objective, the other one practical. Objective: checking ID for buying cigarettes is to prevent under age people from smoking (let's not discuss if this method works or not), whereas in the case of flying the objective can only be commercial by the airline to prevent people from selling their ticket to someone else. Practical: once the age check is done for cigarettes the "prevention" is over. For tickets there is little chance for a grey market. For it to happen on a large scale it would be widely known and could then easily be stopped. Or it happens on a much smaller scale, but no "broker" would take the risk to buy tickets and only have a small under-cover market to which he can sell them. If it happens within a family or similar this is really very small scale and frankly, if I was the airline I wouldn't care if I fill my plane with daddy or son, the hypothetical loss is much smaller than the non-hypothetical money it costs me to check IDs and to have longer turnaround times.

It is not because one idiotic solution exists than other idiocies are justified. Train operators would just need to put pictures on their cards, end of story.

We may differ on what a "problem" is but since there are zero benefits but huge costs for airlines and it's a hassle for passengers there's no reason to keep it.

Yes. But the world has moved in that direction anyway, where your smartphone more and more becomes a holder of ID for all sorts of commercial and non-commercial interaction. Having the BP on your smartphone already brings things down to a one-device solution.

EDIT: just read orbitmics's post. Absolutely concur with what he writes.