As you noted, but for the record and for emphasis, Markup's discussion of headline tags includes the statement "Please note that <h1> and <h2>are discouraged here.</i>."

Failure to honor that guidance does NOT, IMO, amount to a case in which "someone misbehaved again...." where my understanding of the connotations of this usage of "misbehaved" include "deliberately flouted the rules." I suspect this is more like the case of the AM or noob who ignores the guidance re para tags posted (even more prominently) at our text-entry box.

As to the merits of disabling <h1>, 2 & 3 -- my $0.02 worth is that even if use were regarded as a mortal sin, felonious mis-formatting, or some other semi-egregious violation of the Monastery's generally accepted conventions.

Take a node that's been posted in ALL-CAPS as a parallel (a sorta' weak onethough because (IME) the whole internet community pretty much subscribes to the notion that doing so is rude ('shouting!'). That happens here at least as often as the use of the larger headline tags but we probably can't cure the problem by disabling upper-case letters... and its probably not worth the trouble to build a filter that will correctly revise an all-caps node.

And finally, you've already mentioned what seems a reasonable solution: let those who chose use CSS to specify rendering a headline tags at less-than-pure-html size but add no needless complications for pmdevs nor any new Monastic mysteries for those who don't share your objection to the current rendering, or who (were we to adopt the option of site-wide css modification of h1 and h2 tags) wouldn't understand why theirs came out so small.

> Any CSS-suggestions for H1..H3?

FWIW

these are my styles now in Display Settings.

h1 { font-size: 1.3em; color: #800000; }
h2 { font-size: 1.2em; color: #800000;}
h3 { font-size: 1.15em; }
h4 { font-size: 1em; }
h5 { font-size: .95em; }
h6 { font-size: .9em; }
[download]

Not perfect but a start (margins etc are missing¹).

Though good enough to easily read posts on my mobile.

Thanks to the dark-red color I can easily identify <h2> in posts like How (Not) To Ask A Question.

YMMV! :)

You are free to suggest improvements.

¹) well I'm not a designer ( yes, excellent sperm count :)

Why do we allow <h1> tags at all?

So that they can be used :) like for headings and such

Posts here are used for a lot of purposes, including articles and papers which might indeed require markup.   Yes, sometimes those are used to “shout.”   But that alone doesn’t justify getting rid of the facility.   Perhaps some of the tags are a bit too large, take up a bit too much screen-space and so on, but that is aesthetics.   Some of the “threads” that get posted here are, effectively, publications.

I don’t have any specific suggestions other than they probably should be only slightly-larger than the normal font that is used on the site, and with less vertical margin space.   Variations in boldness, italic, serifs and so-on can be used to vary the tags without burning-up column inches.

h1

On the one hand, that’s probably pretty-good markup for a document heading.   But, particularly on a small screen, that is a lot of real-estate being consumed gratuitously.