It's generally an option for those who want to declutter or store a proportion of their goods for a short amount of time.
For example, the thin walls of standard moving boxes cannot withstand the multiple transfers, stacking and other rigors of the shipping / mailing process.
Many mail storage companies charge re-boxing and handling fees for boxes that are poorly packed or damaged on arrival.
In the US, many companies have launched and continue to offer services today, while a few early innovators are no longer in business.
The market has quickly evolved to become specialized, with a number of variations on the initial Mail Storage concept currently being offered.