Online check-in and kiosks seem to work pretty well all over Europe. Can't recall the last time I used LHR and didn't use a machine. Indeed the best combination is online check-in, then just use the machine to collect boarding pass.
(Gasps heard from Qantas people: "Online check-in? What's that? Next they'll be letting people choose their seats before they show up at the airport!")
Haven't used BA's print-your-boarding-pass-at-home yet, but my first shot can't be far away.
Most airlines limit online check-in to situations where they can do checks - eg. member of FF scheme, paid with same card, etc. Sure it's not infallible but neither is the eyeball.
It does put more pressure on the guys at the gate (who do the final ID check throughout most of Europe, in my experience) - but that it where the pressure should be. That is, I really don't care if name & ID match at check-in; I DO care that the person who actually boards, is the one in front of me. The check-in ID match is a nice check, but at airports where there are lots of transit pax mingling, the chance of abuse is high. Best to check at boarding.
As for security, the whole airside area or gate area should be sterile (again, depending on transit arrangements) so checking ID doesn't really come up as an issue with respect to check-in arrangements.
I suspect the real weakness is how well the gate agent checks ID. I have had some sets of eyes look right into my soul whilst others may have been Ray Charles... but in both instances, the attention given to the check tended to be consistent with the apparent attitude to safety across the whole airport.