One would store Bitcoins remotely for the same reason they would store other valuable data: convenience.
Stuff stored in the cloud can be made available anywhere and may provide services such as encryption, redundant storage, backup, search, etc.
But, the downsides must not outweigh the upsides. The bar is high in that regard for storing a lot of Bitcoins remotely because, for me, I would not use such a service unless:
1. The service provided is from a reputable, trustworthy business
2. The service encrypts data locally before uploading, preferably with an open source program that does not change often
3. There is some sort of external auditing to verify the company is providing the services promised (such as backups)
4. There is convenient integration with my local wallet(s)
And there are probably other requirements that I am not thinking of right now. I am not aware of any such service right now, but I am a Newbie, so don't take my word for it.
If the data is encrypted locally with a program you can trust, security would mostly be under your control. Otherwise, for me, there is no company on earth I would trust to properly transport, encrypt, and store my valuable data in a secure way.