It is meet that you should use Latin as a fine example of a highly developed language. similar examples can be found in all liturgical languages besides Latin, such as Greek, Church Slavonic and Hebrew. English, German, etc. are civil languages, somewhere between Cockney type slang and liturgical languages, endowed with some flexibility but not fully.
Modern Serbian is a cockney style dialect, a peasant language elevated to a status of a literary standard, forced to borrow words form left and right, and much more at home with phraseological expressions that with those containing participles.
The Church still uses some of the "archaic" or "outdated" expressions such as блаженопочивши or свјатејши, but that is looked upon as vestige of tradition reserved only for Church terminology.
The First Serbian daily newspapers, Новине Сербске, was printed in тхе city described as "Царствующа Виенна" at the turn of the 18th into 19th century. Today, this expression would be utterly impossible. Instead ne would have to say "Беч (modern name for Vienna taken from Hungarian) који царује", although the participle "царствујушћа" still exists. Rather one would use the adjective Царски Беч.
Likewise, the first provisional Serbian government established following the first Serbian Uprising in 1804 was called Правительствующій Совтеъ. Today, interetsingly, one could still use a participle for Руководећи савет, but if one is to you the word managing rather than leading, one has to use phraseology, as in Савет који управља.
Still it is a matter of choice. Serbian is not inherently uncapable of parcticiple use, it is for whatever reason not in vogue.
In English there were times when simple “telegraph” style of speech — think of Hemingway prose — was considered low-class. Linguists tried to inculcate the use of complex flowery vocabulary (citation needed, as Wikipedia would say, but nothing comes to mind by way of example). In Russian Pushkin had that revolutionary attitude that the simples expression is also the most beautiful. Today in English simple short sentence structure is in vogue, as it is you say, in Serbian. But this does not make English inherenty a more primitive language than it was in the times of Daniel Webster. It may, one day, swing back.
Overuse of participles may at times sound archaic in Russian as well.