The practice of translating foreign monarch's or noble's name

Probably has much to do with phonetics, and of course in case of different alphabets errors in transliteration.
So Karel in Dutch becomes Karl in German, Charles in French and English, Carlos in Spanish.
Nothing to do with them being royals, it happens with all names (and other words).
I never give my actual first name to foreigners who don't speak my language as it's pretty much impossible to pronounce correctly in any other (the phonemes don't exist), giving an equivalent instead. And that too is common across history, with people historically often giving foreigners Latin equivalents of their actual names for ease of international communication.
That current rulers are typically referred to by their actual name probably indicates nothing more than that global communications have made it more likely that people will know how to properly pronounce those names, and/or have access to original spoken sources rather than records passed by word of mouth or written down by semi-literate clerks and emissaries.

In Russian there is a similar convention. For example, we refer English monarchs by German-like names.

I think the origin of this convention is pragmatism. Many monarchs changed their country by marriage. Some monarchs were sovereigns of two or more countries with different language. As such it is difficult to define the "true" ethnicity of many monarchs without offending other peoples.

In my opinion the reason is that all Europe (except Turkey and some other minor Balkan areas) is influenced by Christianity. This religion was for many years the most common factor of all European people, never mind if it was Catholic, Orthodox or Protestant.

Because all Europeans were joined by this common faith, they shared the same God, the same tradition (or Tradition if you like) and for many years also the official language -- Latin. The Christianity comes with the idea of "saints" after whom, to honor them, people name their children.

Because English John, German Johannes, Polish Jan, Italian Giovanni etc. are to honor the same saint, each use of English John was translated to German Johannes because it was the same name of the same saint. In Latin all of names (both first and last) are translated (in modern times you can see this in biology species' names) and this was common practice in all countries in the world (by "world" I mean Europe here). It was not only for nobility, rulers and saints, but everyone, but in fact this "everyone" was for long time the educated people, so nobility and clergy.

In 19th century it was still common practice to translate names of writers, scientists and rich people (bourgeois).

At the moment it is not common practice, I think because of laziness of journalists and other media people, who don't want to look what "Jose" means in English, and use original names in tv and this is no kind of problem if you're watching news that you will forget in an hour.

The other factor is that at the moment, when Christianity is not that important, one can (especially in America) name his/her child for example "Table" or "Jahdadweqw" and this is no problem to translate in the first case (but is this "table" a furniture or a tabular grid of data?), but quite impossible in the second -- although you can use a Google translator now, but not 20 years ago.

So I think that translating rulers names, as well as popes and saints is still a part of tradition. Not translating the names of normal people comes from laziness of (first) journalists, (second) all of us.

In Polish (my mother language), but I'm pretty sure this could be also in peoples who are admired by foreign habits, there is also a feeling, that if something is not ours, it is better (I'd rather say "it was", in 1990s. when the communism has fallen and this was some adoration of Western style of life as only an opposition to Eastern style of life). So when you say "Nicholas Cage" in Polish it's something great, but you never think what "cage" means.

And according to your question, the same "laziness" is now made for rulers/nobility names as for other "normal" people.

At the time Europe used to be called Christianity. Most if not all monarchies ruled by divine right. All names were officially in Latin so each country translated it in its own vernacular language, even if some names had obviously no Latin origin (Karl, Otto, etc) :

Franciscus =>> François / Francis / Franz/ Francisco

Carolus =>> Charles / Charles / Karl / Carlos

And even today the Pontifex maximus emeritus (whose official name is in Latin) :

Benedictus =>> Benoît / Benedict / Benedikt / Benedicto

The translation was necessary because, unlike in most european languages, Latin names are subject to declension, and because the spoken Latin wasn't the same everywhere.

However, the current monarchs of Europe have their country language as official language (England still have some French but at least since Napoleon it's widely ignored). So, since the early 20th century (few people spoke of Emperor William II) :

Juan Carlos, Elizabeth, Prince William, Beatrix, Wilhelmina, etc...