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.