The reasoning is twofold
In the case of instruments that transpose in octaves (Like guitar, which actually transposes an octave up from written), the transposing convention began so that instruments with high ranges didn't have to read notes constantly on multiple ledger lines above the stave. It makes it much easier to read.
In the case of instruments transposing between keys and semitones and stuff, they transpose so that players who are used to one instrument in that family, don't have to learn new fingerings to play the same notes on other instruments in the family. (IE A bassoon player playing an Oboe part doesn't have to learn a new fingering to play a note written as C, he can use the same fingering for both, and the composers transposition within the score will make sure he's playing the right pitch.)
This allowed composers to use the same musicians for multiple instruments easily, rather than having to bring in a new musician for each new instrument. The composer just compensates for the transposition within the score. Its much easier for a composer to do this, than it is for him to bring in multiple new musicians, or for instrumentalists to learn new ways of playing their instrument.
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