You could scan and save them for future generations. As the family genealogist, I can't tell you how excited I would be to get a stack (or scans) of my grandmother or great grandmother's letters - good, bad, and everything in between.A job waiting to be done.
Before throwing them out, I promised my siblings to read through all my mother's letters (boxes of them) and to put together everything that's interesting, funny, forgotten or even philosophical for future generations. We decided not to include extremes: she had a tendency to divide people (including her 6 children, sons- and daughters-in-law and grandchildren) into two camps: the angels and the witches. Funniliy enough the menfolk were always among the angels but the females, if they were lucky, were allowed a temporary residence with the angels, though some poor women and girls never left the witches den. It doesn't make very good reading but there are some gems among the little stories she told.