it depends in large part on who you impute the speaker of the error message to be, and who the listener
if i say to you 'i'm sorry my email was so long' that question doesn't arise; you know who the speaker is and who the intended listener is. similarly, if your browser says to you 'i'm sorry my email was so long', as it is doing as you read this, hopefully the surrounding context contains enough information to identify the purported speaker and intended listener. (i'm sorry my email was so long!) it is 'quoted speech', as when lisa says, 'and tanya was all, "i'm sooo drunk right now! oh my god, i'm like sooo sorrryyy!" and we laughed'; lisa is not apologizing, tanya is.
but what agent does a running computer program represent? or, on whose behalf are its error mesages speaking?
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in the case of, for example, a built-in macos program, this is clear: it represents apple, the corporation, a fictitious collective identity like the dread pirate roberts, anonymous, or bourbaki. in exchange for your money, apple is providing you a service by allowing you to run that software on the computer you nominally bought. the computer program, written or at least patched together by apple programmers, speaks with apple's voice
therefore, if apple cannot fulfill your request, it would be polite for apple to express regret, in the program's error message, for letting your hopes down. perhaps it could include a link to the web site where you can purchase the permission to use 'your' computer to think the thoughts you are not currently licensed to think in it. this applies generally to proprietary software that you are not allowed to fix, as vanderZwan suggests. (even if you can figure out how to fix it, apple is responsible for making that unnecessarily difficult by, for example, not supplying you source code and checking executable signatures.)
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traditionally, though, on conventional timesharing operating systems like unix, the programs are considered to be an extension of the user's mind, as a bicycle is an extension of their body, and thus they represent the user's agency; they carry out the user's own will, not the will of their programmers. a program that carries out the will of its programmer, where it conflicts with the will of its user, is considered a 'trojan horse' or 'malicious', with narrow exceptions; and strong social sanctions are attached to distributing such programs. the protection mechanisms in the operating system simply assume they don't exist
so, in that social context, if a program is speaking to you, it is speaking to you on your own behalf, like a note you have left yourself in your day planner. perhaps tex does not have enough string space to interpret a given document, because you compiled it to have less string space than that, or perhaps you chose to use a copy of tex a colleague of yours compiled, to save the time and disk quota of compiling it yourself. that is no different from your example of contradictory declarations in the input; all that is needed is pointers to the mutually inconsistent limits (ran out of string space at bar.tex line 5329, string space size is defined in foo.web line 30213, compiled on 01994-10-31 from the source tree in /u3/schaker/new-tex)
should cannondale apologize to you when you fall off your bicycle, or arrive late to a meeting, or ride into a slum and get mugged? if you open the kitchen cabinet to get the table salt, and find that you have left it in the dining room, will you apologize to yourself? when you reserve time in your day planner for a meeting you expect to be unpleasant, does the calendar entry begin with "i'm sorry"? should don knuth apologize for not making the string size allocation larger? surely not. even schaker probably should not; if you want a larger string size allocation, you can recompile tex yourself almost as easily as schaker can
but it depends on the social context. perhaps if schaker is responsible for maintaining the tex installation all the math professors use, the error message should include his email address so they can request a dilation of their tex
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in general, in free software† the app's programmers are not responsible for its behavior, unless they have somehow contrived to conceal it. you, the user, are fully empowered to modify the app to manifest your own agency, and responsible for doing so. so the traditional timesharing situation holds
a precondition for a sincere apology is accepting responsibility for the situation being apologized for—which implies that the intended recipient of the apology does not have that responsibility. in free software, a maximally uncharitable interpretation of an error message (other than for an internal bug) saying 'i apologize for' (or, worse, 'we apologize for') is a red flag that the developer is a renegade who rejects this social contract; they are attempting to arrogate the right to determine what you may and may not do with your computer, by virtue of having written some of the software you are trying to use to do it. like ayn rand, they consider themself an atlas on whose shoulders the mere user is generously permitted to ride, as long as they do not shrug. they consider 'trojan horses' to be normal software. this is not a collegial or collaborative relationship
but that is a maximally uncharitable interpretation. perhaps the programmer is apologizing because they felt that they left a job half done, or they would have liked to find a smoother way to handle a different situation, and just couldn't figure one out. or perhaps the "sorry" is not really an apology, accepting responsibility, but merely an expression of sympathy for the users who find themselves in an unfortunate situation, without respect to whose responsibility it is
but, with respect to error message design, it is an immense blunder to generalize from the social context of proprietary software like xcode to the social context of free software like gcc
of course, in some situations, free software on a shared computer is instead an instrument of some office administrator or similar, who is the agent responsible for the unfortunate situation that might merit an apology. in that case the desk phone number and email address of that administrator ought to be included in the error message, in the interest of solving the problem as expeditiously as possible if it is urgent to the user
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while it can be amusing for computer programs to present us a theater in which various personages portray different personalities—some servile, some compassionate, some aggressive—artistically that can be done well or poorly, and it is important for the user to understand that these personages are fictional, and that a conventional computer program is merely an instrument, not an agent
different users' tastes in such theater may vary; judging from popular novels, movies, tv shows, video games, and rap music, most prefer fiction containing passionate, aggressive personages who struggle to the death. portraying such personages in error messages would surely be entertaining (japanese video games often do this, launching insults at the player character when the player suffers a misfortune they could have avoided) but it might occasionally cause difficulties when a user appears who does not understand that the program is not itself an agent, and anyway if done without artistic skill it will not be entertaining at all
on the other hand, the stackexchange thread seems to recommend always portraying agents in error messages and always making them servile. this compounds that risk rather than ameliorating it: it is commonly done without enough artistic skill to render it entertaining; it adds the extra challenge of making a servile personage sympathetic rather than merely irritating; and the motivation given in the stackexchange thread insults the user by the unspoken implication that they are unable to distinguish the fictional personage portrayed in a computer program from a real sentient agent—an implication that may not be apparent from a single error message, but which will surely become evident over time unless the user is very small or socially handicapped
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† perhaps we should rename free software 'nontoxic software', given that the movement to rename it 'open source' has not been as successful as was hoped, and 'free software' was always unavoidably a very confusing term