The essential difference for me, check-in agent vs machine, is the security element. You perceive no difference, yet I do!
The check-in agent is better equipped, and better able to identify a passenger who is unfit to fly through illness, drink, drugs or underlying mental impairment. A harrassed (and often bullied) Gate Team pressed by their managers to achieve an on-time departure at all costs may very easily fail to spot (or choose to fail to spot) a passenger who could well be a hazard to the safety of the flight!
Security staff are also not solely to be relied upon in this regard - if you observe the average security firm in this country (Britain) (whether airport related or not) the majority of security staff are middle-aged ex-servicemen or elderly people with a good employment record (but just looking to fill the gap between redundancy from their last job and retirement!) The airport security guys are used to being ridiculed by the airline management if they do bring something to attention and are more being used to look pretty and instil some confidence into the travelling public than anything else!!! (But, of course, first and foremost they are to look after the security of the airport shops!!!)
Yes - BTW - I am referring to bags travelling ahead of the passenger. US carriers at Gatwick are doing this on a regular basis, both inbound and outbound!!! I am aware of this because of our connecting passengers where, very often, we receive the bags but the passenger hasn't actually travelled!!! On talking to their baggage agents, it transpires it is a regular occurrence and, in any case, it is perfectly permissible for US carriers to allow this for "Stand By" pax - the FAA and "Homeland Security" doesn't seem to have an issue with this!!!
Now - what I say about self-service is only my opinion, and your opinion is your own! Only time will tell which of us is right!!!