What are the historical, orthographical and etymological reasons for this? I checked Wiktionary says it is from Middle High German hērschen with one r.
The verb herrschen is derived from the noun der Herr (mister, master, lord). Der Herr was the leading person of a group. Among christians der Herr is even used as a synonym for god (very similar to the English lord).
The verb herrschen means to govern, to rule, to dominate (to dominate is derived from latin dominus = German Herr = English lord)
And it is true. In Middle High German (MHG) the verb had only one R and a long E:
But this is the MHG version of Herr:
So both words was written similar at same epochs.
In German the number of written consonants at the end of a syllable indicate the length of the preceding vowel. Two or more consonants indicate a short vowel, and a double consonant counts as two consonants. Only one consonant or no consonant at all indicates a longe vowel. (There are exceptions, but this rule is true for the vast majority of German words)
So, when the former long vowel E becomes short over the centuries, this change of pronunciation induces a change in spelling: the number of written consonants after that vowel needs to be increased, and since there is only one spoken consonant it has to be written twice.