Other than the saddle being the small little piece of hard wood at the bottom of the violin that the tailgut sits on to prevent the table (top) of the instrument getting damaged it has a sonic function as well.
If the height of the nut is low then the angle of the tail piece will increase which would cause the pressure on the table to be greater resulting in a brighter tone. The opposite causes the tone to dampen. In some cases with instruments that have too much power and uncontrollable boom this can be manipulated to regulate the sound. This would probably be further down the line after having worked through some of the other sound altering possibilities.
Note. A well snug and tightly fitting nut is not wise and can be seen on many instruments where cracks develop on either side of it. These cracks can travel all the way up the instrument which can cause a sound post crack, if on the treble side, or a crack close to the bass bar on the bass side. Both of these are unfortunate cracks to have and are better off not created with a perfectly tight fitting nut from the start. The reason for these cracks developing is mostly because of environmental wet and dry seasons causing the two different woods to expand and contract.
For a seemingly insignificant piece of wood it has its worth, effects and dangers.