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Why is it so that there are often two identical oboes, two identical clarinets, two identical bassoons and two identical trombones in a symphonic orchestra?
Is it just because one instrument is not loud enough and both are always playing exactly the same line? Or does each one of the pair play different lines?
Both. When they play in unison it’s louder. When they play separate lines it’s a richer sound. There’s also usually two flutes, two trumpets, and four French horns.
And I think the word “identical” might be overstating it. Yes, generally the second chair will be asked or expected to play the same or similar make and model of instrument, but no two instruments or players are identical. Having the slightly different tone between the two instruments adds to the richness of the orchestra.
It’s similar to there being two violin sections. And 6-10 violins in each section. They can play together or divisi or one can play solo, etc.
The overall size of the orchestra is to fill the concert hall so everyone can hear in a time before electronic amplification. The relative numbers of instruments create a mostly balanced level across the orchestra, at least within reason.
Studying scores while listening carefully to symphonic works will help make this all clearer. Also going to see live symphonic music would give you a first hand understanding.
Much (?) more frequently they play different voices; note, that as for all wind instruments only one tone can be produced at the same time. So if the composer desires an additional tone of that same color, there is no choice but to add another player. The first position typically has a bit more to play, especially in pianissimo he/she may play alone.
(For super-difficult passages the conductor may even instruct the player of second instrument to stay silent in unison passages, since differences are far easier to spot than wrong notes. This, as correctly commented, is no issue for professional orchestras, but applies to student and amateur ensembles.)
My understanding is you have enough players per instrument to cover the number of written parts, except for the string which used large numbers of players, not because there were many more written parts, but for the special timbral quality of a large group of strings.
Lots of classical symphonies have just two parts per wind instruments. Two parts meaning two notes to be played simultaneously. So just two players was enough to handle to two written parts.
Strings were different. Especially the violins. Lots of violins were used. Not because there were many more written parts, not for volume, but for timbre. The group sound is "richer", "warmer", also the bow attack become a little softer, more diffused. However you describe it a large group of strings sounds timbrally different that just one string player per part.
You can also think of it in terms of instrumental genres too. The symphonic orchestra is essentially a string orchestra and the winds just augment that string orchestra for timbral color. The large group of strings distinguishes the symphony orchestra from instrumental groupings like a concertino group in a concerto or chamber ensembles like a string quartet. So, many strings versus single string players distinguishes some genres, but the number of wind players doesn't. You only need the number of wind players to fit the number of wind parts.
In my mind that makes the distinguishing factor about how many players per instrument to be mostly about the timbral expectations of various instrumental genres.
Reed instruments have keyed pitches. As opposed to bowed strings (and incidentally, trombones) that means that to a certain degree the pitch relations between instruments with purportedly identical pitch are mostly fixed, but since expressiveness and volume typically impacts pitch as well, expressive melody lines don't add up to a rich complex texture like with violins (also aided by a comparatively rich overtone spectrum) but contain some non-organic semi-systematic beatings. At the same time, any multiplication of instruments diminishes expressivity by averaging it out.
2 is a compromise that still provides redundancy (and differentiation from a solo voice, even though orchestral woodwinds are all expected to be able to carry a solo, something not to equal degree the case with strings) while not attempting to compose a complex sound texture which does not work all as convincingly with reed instruments as with some others.
I am fuzzy about trombones.
