Writing music is not dissimilar from writing spoken language. Faithfully representing the sounds is important, but it’s not the only aspect that matters. For example, you can
technically insert a line break anywhere you want without changing the meaning of a text, but it would be confusing to the reader to in-
-sert a line break in the middle of a sentence or even a word.
Similarly, the time signature in music helps keep the formatting and “punctuation” of the music sensible. Sometimes this is obvious – if a song has a 3/4 feeling but is written in 4/4, you will frequently have phrases extending over the measure line in a way that requires awkward notation.* Sometimes it’s more subtle. Both 6/8 and 3/4 can have a triplet feeling, but they put different emphasis on different beats.
*To get technical on this point, consider a repeated phrase of one quarter note followed by one half note. In 3/4 time, it is obvious how this phrase repeats. Each bar will have the same metrical pattern. In 4/4, you would instead get the following cycle of bars:
1. Quarter, half, quarter
2. Half, quarter, quarter-tied-to-
3. -quarter, quarter, half
When playing a piece of music that they’re not already familiar with (and if they are already familiar – sheet music doesn’t really matter!) it matters a lot for a musician to be able to peek ahead and register “OK, I have 8 bars of this pattern” rather than having to parse that 3 bar cycle and realize that it’s a repeated pattern too.
Latest Answers