iOS indeed has some stupid limitations, e.g. no access to files within app sandboxes and no shared folder.
However to get around this, get the
free Documents app.
It can, beside connecting to well known 'cloud' providers, also sync with SSH (SFTP), FTP, SMB (Windows share) and Webdav in the same (wifi) network.
As a bonus is also plays movies and music without the stupid iTunes database and does not require iTunes and can be put into this app's space just like any non-Apple music player. Files stored in that app can be down- and uploaded with Safari and sent / received by the default Mail app, so it also bypasses these limitations.
So when using a Windows computer, just share a folder and connect to it from Documents and upload to (or download from) your computer. The standard iOS Photos folder is also accessible.
When you have a Mac, you can better use SSH (Preferences => Sharing => check Remote Login) which is faster, but SMB ('File sharing' in the same preferences pane) also works.
For me this works flawlessly with my Mac, better than the propietary Apple only syncing tools.