It can be helpful to think of the written music as being a guide only: compare classical music with folk, rock, jazz, pop etc, where the concept of playing a "cover" comes in - musicians playing their own perception or interpretation of a piece, with amazingly different outcomes....and yet the theme will come out, and we recognise it for the same, or at least as being essentially the same one. The written music is effectively a framework for the musician's performance: it indicates key, note order, rhythmic structure, and separately from that too, the pulse - and even then, not always. There is music from renaissance times which has a pulse but no bar lines, there is music from early baroque which is free-form, in which notation is only ever intended to convey an approximation of rhythm, and sometimes also uses conventions regarding accidentals which are now obsolete but were known to musicians of the time (the concept of ficta
). Leaping right through, coming to modern times, there is written music which gives the performer considerable leeway to "invent" things - I've played several pieces in which one produces a random chatter of notes, in one case indicated on the score only that the overall impression of pitch must rise, but not which notes, nor accurate timing.
Thus, as the others have said, it's about producing a performance with shape - and if dynamics are not marked, then it's about showing an awareness of phrase, for instance by "growing" in volume as pitch rises, or by articulating a repeated phrase as an echo the second time round, more softly. It's an art, and as such, scientific notation cannot be more than a guide: a uniformly even volume will have less to hold the listener's attention than one which gently follows phrases.
I actually don't like "hairpins" anyway - they're always straight-lined, and in my experience crescendi and decrescendi are better not being made totally evenly graded