It's true that 'as regards' is less common and somewhat stiff and formal. (Altmodisch, beamtenenglisch, yes, that's about right.) So it may be unfamiliar to some people, but it's still entirely correct. The syntax uses 'regards' as a verb in the present tense, which is why it has an S:
as regards X
In English, to help explain the grammar, you could paraphrase it with another verb: it means 'as concerns X,' or 'as relates to X.'
In German I'm just guessing, but maybe something like 'wie es X angeht / betrifft'? Or in the passive: 'wie X betrachtet wird'? (Of course the idiomatic translation would still be 'bezüglich,' 'hinsichtlich,' etc., but to understand the grammar it often helps to think of something with similar syntax.)
Nowadays the more common form is simply
a verb that has in practice become a preposition.
If anyone suggests substituting 'regards' with an S after a preposition, they're only revealing their own uncertainty about grammar. The other more common phrases in fact have no S, because they're nouns:
in regard to X
with regard to X
Here, 'regard' means literally something like 'Betrachtung' or 'Anbetracht.' (Though of course, again, it may be more idiomatic to translate it as 'in/mit Bezug auf,' 'bezüglich,' etc.)
If you added an S to the noun 'regard,' it would change the meaning completely, to 'greetings':
with regards to X = mit Grüßen an X
As you've discovered, though, there are quite a few native English speakers who don't understand that. Maybe now you can help them out. (-;