I think Ryanair gate announcements inform passengers that boarding passes will be checked again on entering the aircraft but I can't imagine that this is taken in by all passengers.
I once wondered why my boarding pass was checked at the top of the airbridge/jetway and again at the aircraft door but when I queried it was told that someone with access to the tarmac - such as an airside worker - could board the aircraft via the steps which connect the airbridge with the tarmac. Non-allocated seating presumably would make it less likely that such a person was discovered - unless the 'plane was full! - and so I can appreciate why airlines which operate such seating are particularly keen to ensure that only the correct people are permitted onboard. (Obviously, with non-allocated seating, airlines such as Ryanair and easyJet have no idea who is sitting where. I remember a farce a year or two ago on a STN-AMS easyJet flight with one passenger too many; it took absolutely ages to locate this person, there was recount after recount. On this 35 minute flight the delay made quite a difference. All credit to the staff for not departing before the issue was resolved, but allocated seating would have made the situation easier to deal with. Rant over!)
P.S. I recently saw a cabin attendant at the door of an easyJet aircraft at Madrid ask to see a passenger's passport. I wasn't asked nor were any of the passengers immediately ahead of me (apart from this one person). Curious! What was that all about?!