I think a lot of CoCs contain the "buzz word" may, i.e. if you do not arrive at check-in xx minutes before departure, you may not be able to board your flight. Some may be more firm than that.
In any case, I take the view that if you arrive at check-in after the cut-off, you are not guaranteed to be checked in (yes, I know that can happen even if you do make it on time, e.g. bumps, but let's keep the argument simple here). If the airline checks you in after this time, fine, but if they decide not to, then you are in no capacity whatsoever to complain.
It comes back to the point many have raised here - you need to draw the line. It's moot for airlines to suggest "grace periods", because people will want graces on the grace periods, etc.. To put it in the words of a random generation, "Be there (on time) or be square!"
Of course, this will never stop people from complaining when they're in the wrong. Making a complaint about airline practices that'll end up in the press is like shooting fish in a barrel.