Our new Magento host won't allow full FTP access. At first they wouldn't allow any FTP access (to our own website,) but then offered very limited access to a certain folder.
Is this normal? Normally, we have always had FTP access with other hosts. I occasionally use FTP, plus quite often like to have a look around the server space (of our own website.)
I have spoken to them again. They will allow restricted FTP access to a folder for stock uploads. I have asked about full FTP access, and they said they would allow it if asked for, but recommend against it, as they could be held responsible if 'anything goes wrong.'
What type of hosting service are you using?
With most hosting providers you will have full access to all files and database but if you are using a SaaS service, they may not allow you access to any files at all.
Another possibility that I can think of is that your "host" is just reselling from somebody else and they are cramming all websites into an account, which is why they can only limit your access.