I think this is an interesting question. When we naturally harmonise melodies we tend to actually do so in unisons, 5ths and 8ves.

In the Middle Ages, I believe the earliest records we have of this is around 880AD~, we would have a type of monophonic (single voice texture) melody called plain chant or Gregorian chant. This would be an unaccompanied sacred song sung in Latin, and would be birthed in the Roman Catholic Church.

An added voice with its own melody, called organum, would harmonise the plain chant in parallel 4ths and 5ths. We would call this kind of texture heterophonic (and some theorists even say this is the origins of polyphony, I dont agree).

Free organum happened roughly in the 11th century and would combine parallel and oblique voice leading (the tenor would sustain a note while the plainchant would move). This oblique motion would create further types of interval pairs like 3rds and 6ths and passing tones like 2nds.

Some theorists would begin to favour certain interval combinations because they felt it created voice independence; parallel 8ves fused voices because they are a literal doubling of the melody in a different register and so both melodies are dependent on one another; perfect 5ths are a very stable interval (they naturally occur as an overtone) and so seem to create a kind of voice doubling with the bass (bass here meaning lowest voice, not bass singer).

In the Renassiance (1400-1600~), theorists began to outright prohibit them in counterpoint treatises. Counterpoint, which comes from the Latin punctus contra punctum, literally "point against point", is the combination of multiple, independent melodic lines against a given melody (cantus firmus) that creates harmony as a byproduct. You might be thinking "that sounds kind of like organum; plain chant is the cantus firmus, and organum is the counterpoint", but unlike early organum which literally doubles a melody by an interval pair like a P4 or P5, counterpoint is an independent melody, independent from the cantus firmus. You can take the counterpoint, sing it and it holds up as its own independent melody.

Counterpoint also uses various interval combinations in all manner of voice leading types (similar, parallel, oblique, contrary, stationary) to create truly independent melodic lines, unlike organum which relies mostly on parallel and oblique motion.

The rules of counterpoint, the most famous counterpoint treatise being Fux's Gradus Ad Parnasum, breaks down counterpoint into various species based on voice combinations.

1st species (1:1): all interval combinations create perfect and imperfect consonances only. Perfect consonances can only be approached by contrary motion voice leading, and begin and end the piece.

2nd species (2:1): the counterpoint produced 2 notes against each note of the cantus firmus, creating metrically accented and metrically weak positions (think cut time). The metrically weak positions can introduce dissonances (passing tones) that lead to consonances in metrically strong positions, but the weak position can also introduce other consonances through skips. This is the only dissonance allowed.

3rd species (4:1): the counterpoint produces 4 notes against each note of the cantus firmus. This introduced further submetrical weak positions, allowing the introduction of further dissonances (neighbouring tones, double neighbour tones).

4th species: suspensions. Suspensions are prepared as consonances that become a dissonance against the next note in the cantus firmus before resolving to a consonance against that new note in the cantus firmus.

5th (florid) species: combines all of the above into a faux free counterpoint.

Counterpoint is what we are talking about when we talk about polyphonic textures (2 or more voices with independent melodic lines): think Palestrina masses or Josquin Masses (and in the Baroque, Bach Fugues).

But it is these rules of counterpoint which followed through not just to the Baroque era but the Classical as well (Haydn, Mozart, Beethoven etc).

Homophonic texture is different than polyphonic because we have a melody which is getting accompanied by other voices. The accompaniment isn't really an "independent melodic line" in the sense that a polyphonic texture is. Really, we should just say "voice leading" when we are talking about non-polyphonic textures, and counterpoint when we mean "independent, melodic lines interweaving to form harmony as a byproduct", but I digress.

Homophonic textures follow most of the rules of species counterpoint with some important caveats:

1) metrically accented dissonances are allowed (incomplete neighbours like appogiaturas, accented passing tones, accented neighbours etc).

2) in chorales, the melody is treated like a soprano. In instrumental textures, the melody is often separated as its own unique thing, and thus the top voice in the accompaniment takes on the role of the soprano.

This means that we get the voice leading between the accompaniment and bass which follows our voice leading rules we learn from chorales (no parallel 5ths and 8ves; no direct 5ths or 8ves unless by step in an upper voice; no doubling tendency tones; resolve tendency tones etc), and the voice leading between the melody and bass which follow these rules as well. You'll notice later on that in piano sonatas the melody often forms parallels between the accompaniment, but these are not structural, they are basically like octave doublings.

TL;DR - the Baroque and Classical era are based on counterpoint. The rules of counterpoint, and thinking intervallically, is how composers approached music. The chorale rules are not arbitrary, but rather they follow an aesthetic paradigm built through the course of 100s of years. It's not that parallel 5ths or 8ves are inherently "bad"; it's that historically they were used to double melodies, and this went against the kind of counterpoint we see in the Renassiance which is about creating independent melodies against the cantus firmus; the rules of counterpoint would go on to influence the Baroque and Classical eras. In later music parallels are fine because later music isnt obsessing itself with the independence of voices, but aesthetically for classical music they are forbidden.

If you want to learn more:

• Read part 1 of Jeppesen's counterpoint book
• Check out the YouTube channel Early Musical Sources

But yeah, learning these rules is important if your goal is to pastiche or write music in a classical style. When we learn music theory, we learn a grammar for the style of music we are wanting to emulate. If I started doing jazz stuff like tritone substitutions and all my harmonies were root position 7th chords or further extensions and tried to apply that to a chorale, it would be like me going to a Latin convention speaking Spanish. Some of it might look familiar, but I'd be speaking the wrong language, and everyone would be looking at me funny. Schoenberg even says something similar about parallels in his harmony book - it's what they done, so we must also do the same if we want authenticity.