Is it ethical for advisors to automatically coauthor papers?

No, automatic co-authorship is not ethical – irrespectively of the discipline!

The following is from the "DFG Proposals for Safeguarding Good Scientific Practice" (pp.82f, emphasis added), which, for instance, strictly forbids "automatic" co-authorships and gives a couple of common negative examples:

Authors of an original scientific publication shall be all those, and only those, who have made significant contributions to the conception of studies or experiments, to the generation, analysis and interpretation of the data, and to preparing the manuscript, and who have consented to its publication, thereby assuming responsibility for it. [...] Therefore, the following contributions on their own are not sufficient to justify authorship:

• merely organisational responsibility for obtaining the funds for the research,
• providing standard investigation material,
• the training of staff in standard methods,
• merely technical work on data collection,
• merely technical support, such as only providing equipment or experimental animals,
• regularly providing datasets only,
• only reading the manuscript without substantial contributions to its content,
• directing an institution or working unit in which the publication originates

Help of this kind can be acknowledged in footnotes or in the foreword.

In fact, DFG (the German Research Council) requires you to sign strict adherence to this ethical code on each and every grant proposal. Other funding agencies have similar regulations.

Is this really common, and if so, in which fields?

I guess it is reasonably common in many fields. As a rule of thumb, it seems to me that the more applied a field is, the more likely you are to see groups where the lab head co-authors every or almost every paper in the lab. In my field (software engineering), I would say at least 50% - 75% of all groups operate like this. Academia.SE tells me that this is not the case e.g., in Theoretical CS.

Note that this does not necessarily mean that the lab head is added to each paper without contribution (although there are certainly groups where it means exactly that). In some cases, it is just that all research in a lab directly runs through the lab head (i.e., nobody works on research without the direct involvement of the lab head). In such cases, co-authorship on all papers may be academically warranted (but this might actually be the worse practice in reality, as it allows for no growth to independence at all for the PhD students and postdocs in the lab).

Is this really ethical?

I would argue that things are more complicated than you seem to think, mostly because the funding argument that you claim "holds no ice" is in fact not so bad. Your comparison with your parents having sex is pretty silly. Big research labs depend on senior researchers acquiring grant money. This takes a lot of time - time, that said researchers cannot use to write actual papers. Researchers on any level are mostly evaluated via papers. Under these circumstances, if senior researchers don't get a "kickback" on some level from the money they acquire, what would motivate them to write grant proposals in the first place?

There is also the added difficulty that in many STEM fields it is just darn difficult to decide whether somebody has made a contribution (see also here: What are the minimum contributions required for co-authorship). Is discussing ideas enough? What if all the important ideas and suggestions came from the advisor? Oftentimes, the research work of a PhD student is basically an implementation of a high-level plan laid out by the advisor in the funding proposal. In that case, has the advisor not by default "contributed" to all papers?

In fundamental mathematics, at least in France, the custom is for advisors never to co-author (important) papers with their students. If an advisor does coauthor a paper with a PhD student, then it is assumed that he or she had to help the student more than should be expected, and this can prevent the student from getting a job afterward.

This goes to the point of being arguably unethical in the opposite way than asked in the question, as most of the time advisors do have a role (if only of suggesting the question and the angle of attack) in PhD student papers.