Indexes aren't free. They take up storage space and reduce the performance of inserts. On top of that, if an index gets too big it can be really slow, the table needs partitioning instead.
In some applications you might value the performance of insert a lot more than select, and not want to pay for extra storage of the index.
In some applications you might value the performance of insert a lot more than select, and not want to pay for extra storage of the index.