Depends, Dropbox works fine as does AWS etc. It's all pay as you go with minimal up front prices which can be great. They also have clear prices and direct competitors.

However, integrating some highly customized software from a 3rd party is generally a terrable idea. See any school using blackboard. Remember you pay for the work and are on the hook if the company drops the product, raises prices, changes the TOS etc.

At least with public API's your likely to find a replacement or have a good starting point to roll your own.